home > Water purification > The system is not formed. The goal of logistics can be expressed in six rules. Characterization of a system by means of its constituent components

The system is not formed. The goal of logistics can be expressed in six rules. Characterization of a system by means of its constituent components

There are many concepts of a system. Consider the concepts that most fully reveal its essential properties (Fig. 1).

Rice. 1. The concept of a system

"A system is a complex of interacting components."

"A system is a set of connected operating elements."

"A system is not just a collection of units ... but a collection of relationships between these units."

And although the concept of a system is defined in different ways, it is usually understood that a system is a certain set of interrelated elements that form a stable unity and integrity, which has integral properties and patterns.

We can define a system as something whole, abstract or real, made up of interdependent parts.

system any object of animate and inanimate nature, society, process or set of processes, scientific theory, etc., can be, if they define elements that form a unity (integrity) with their connections and interconnections between them, which ultimately creates a set of properties, inherent only to this system and distinguishing it from other systems (emergence property).

System(from the Greek SYSTEMA, meaning "a whole made up of parts") is a set of elements, connections and interactions between them and the external environment, forming a certain integrity, unity and purposefulness. Almost every object can be considered as a system.

System is a set of material and non-material objects (elements, subsystems) united by some kind of links (information, mechanical, etc.), designed to achieve a specific goal and achieve it in the best possible way. System defined as a category, i.e. its disclosure is made through the identification of the main properties inherent in the system. To study the system, it is necessary to simplify it while retaining the main properties, i.e. build a model of the system.

System can manifest itself as a holistic material object, which is a naturally conditioned set of functionally interacting elements.

An important means of characterizing a system is its properties. The main properties of the system are manifested through the integrity, interaction and interdependence of the processes of transformation of matter, energy and information, through its functionality, structure, connections, external environment.

Property is the quality of the object parameters, i.e. external manifestations of the way in which knowledge about an object is obtained. Properties make it possible to describe system objects. However, they can change as a result of the functioning of the system.. Properties are external manifestations of the process by which knowledge about an object is obtained, it is observed. Properties provide the ability to describe system objects quantitatively, expressing them in units that have a certain dimension. The properties of system objects can change as a result of its action.

There are the following basic properties of the system :

· The system is a collection of elements . Under certain conditions, elements can be considered as systems.

· The presence of significant relationships between elements. Under significant connections are understood as those that naturally, necessarily determine the integrative properties of the system.

· Presence of a specific organization, which is manifested in a decrease in the degree of system uncertainty compared to the entropy of system-forming factors that determine the possibility of creating a system. These factors include the number of elements of the system, the number of significant links that an element may have.

· The presence of integrative properties , i.e. inherent in the system as a whole, but not inherent in any of its elements separately. Their presence shows that the properties of the system, although they depend on the properties of the elements, are not completely determined by them. The system is not reduced to a simple collection of elements; decomposing the system into separate parts, it is impossible to know all the properties of the system as a whole.

· emergence – the irreducibility of the properties of individual elements and the properties of the system as a whole.

· Integrity - this is a system-wide property, which consists in the fact that a change in any component of the system affects all its other components and leads to a change in the system as a whole; and vice versa, any change to the system is reflected in all components of the system.

· Divisibility – it is possible to decompose the system into subsystems in order to simplify the analysis of the system.

· Communication. Any system operates in the environment, it experiences the effects of the environment and, in turn, affects the environment. Relationship between environment and system can be considered one of the main features of the functioning of the system, an external characteristic of the system, which largely determines its properties.

The system is inherent property to develop, adapt to new conditions by creating new links, elements with their own local goals and means to achieve them. Development– explains complex thermodynamic and informational processes in nature and society.

· Hierarchy. Under the hierarchy refers to the sequential decomposition of the original system into a number of levels with the establishment of a relationship of subordination of the lower levels to the higher ones. Hierarchy of the system consists in the fact that it can be considered as an element of a system of a higher order, and each of its elements, in turn, is a system.

An important system property is system inertia, which determines the time required to transfer the system from one state to another for given control parameters.

· Multifunctionality - the ability of a complex system to implement a certain set of functions on a given structure, which manifests itself in the properties of flexibility, adaptation and survivability.

· Flexibility - this is the property of the system to change the purpose of functioning depending on the conditions of functioning or the state of subsystems.

· adaptability - the ability of the system to change its structure and choose options for behavior in accordance with the new goals of the system and under the influence of environmental factors. An adaptive system is one in which there is a continuous process of learning or self-organization.

· Reliability – this property of the system to implement the specified functions for a certain period of time with the specified quality parameters.

· Security – the ability of the system not to cause unacceptable impacts on technical objects, personnel, and the environment during its operation.

· Vulnerability - the ability to receive damage under the influence of external and (or) internal factors.

· Structured - the behavior of the system is determined by the behavior of its elements and the properties of its structure.

· Dynamism is the ability to function in time.

· The presence of feedback.

Any system has a purpose and limitations. The purpose of the system can be described by the objective function U1 = F (x, y, t, ...), where U1 is the extreme value of one of the quality indicators of the system functioning.

System Behavior can be described by the law Y = F(x), which reflects changes at the input and output of the system. This determines the state of the system.

State of the system- this is an instant photograph, or a cut of the system, a stop in its development. It is determined either through input interactions or output signals (results), or through macro parameters, macro properties of the system. This is a set of states of its n elements and links between them. The task of a particular system is reduced to the task of its states, starting from the birth and ending with the death or transition to another system. The real system cannot be in any state. Restrictions are imposed on her condition - some internal and external factors (for example, a person cannot live 1000 years). Possible states of a real system form a certain subdomain Z SD (subspace) in the state space of the system – a set of admissible states of the system.

Equilibrium- the ability of the system in the absence of external disturbing influences or under constant influences to maintain its state for an arbitrarily long time.

Sustainability- this is the ability of the system to return to a state of equilibrium after it has been brought out of this state under the influence of external or internal disturbing influences. This ability is inherent in systems when the deviation does not exceed a certain established limit.

3. The concept of system structure.

System Structure- a set of system elements and links between them in the form of a set. System Structure means the structure, location, order and reflects certain relationships, the relationship of the components of the system, i.e. its structure and does not take into account the set of properties (states) of its elements.

The system can be represented by a simple enumeration of elements, but most often, when studying an object, such a representation is not enough, because it is required to find out what the object is and what ensures the fulfillment of the set goals.

Rice. 2. System structure

The concept of a system element. By definition element is an integral part of a complex whole. In our concept, a complex whole is a system that is an integral complex of interrelated elements.

Element- a part of the system that has independence in relation to the entire system and is indivisible with this method of separating parts. The indivisibility of an element is considered as the inexpediency of taking into account its internal structure within the model of a given system.

The element itself is characterized only by its external manifestations in the form of connections and relationships with other elements and the external environment.

The concept of communication. Connection- a set of dependencies of the properties of one element on the properties of other elements of the system. To establish a relationship between two elements means to identify the presence of dependencies of their properties. The dependence of the properties of elements can be one-sided and two-sided.

Relationships- a set of bilateral dependencies of the properties of one element on the properties of other elements of the system.

Interaction- a set of relationships and relationships between the properties of elements, when they acquire the character of mutual assistance to each other.

The concept of the external environment. The system exists among other material or non-material objects that are not included in the system and are united by the concept of "external environment" - objects of the external environment. The input characterizes the impact of the external environment on the system, the output characterizes the impact of the system on the external environment.

In fact, the delineation or identification of a system is the division of a certain area of the material world into two parts, one of which is considered as a system - an object of analysis (synthesis), and the other - as an external environment.

External environment- a set of objects (systems) existing in space and time, which are supposed to have an effect on the system.

External environment is a set of natural and artificial systems for which this system is not a functional subsystem.

Structure types

Let's consider a number of typical structures of systems used in the description of organizational, economic, production and technical objects.

Usually the concept of "structure" is associated with a graphical display of elements and their relationships. However, the structure can also be represented in matrix form, the form of a set-theoretic description, using the language of topology, algebra, and other system modeling tools.

Linear (serial) the structure (Fig. 8) is characterized by the fact that each vertex is connected to two neighboring ones. If at least one element (connection) fails, the structure is destroyed. An example of such a structure is a conveyor.

Ring the structure (Fig. 9) is closed, any two elements have two directions of communication. This increases the speed of communication, makes the structure more tenacious.

Cellular the structure (Fig. 10) is characterized by the presence of redundant connections, which increases the reliability (survivability) of the functioning of the structure, but leads to an increase in its cost.

Multiconnected structure (Fig. 11) has the structure of a complete graph. The reliability of functioning is maximum, the efficiency of functioning is high due to the presence of the shortest paths, the cost is maximum.

starry structure (Fig. 12) has a central node that acts as a center, all other elements of the system are subordinate.

graphovaya structure (Fig. 13) is usually used in the description of production and technological systems.

Network structure (net)- a kind of graph structure, which is a decomposition of the system in time.

For example, a network structure can display the order of operation of a technical system (telephone network, electrical network, etc.), stages of human activity (when manufacturing products - a network diagram, when designing - a network model, when planning - a network model, a network plan, etc. d.).

Hierarchical the structure is most widely used in the design of control systems, the higher the level of the hierarchy, the fewer links its elements have. All elements except the upper and lower levels have both command and subordinate control functions.

Hierarchical structures represent the decomposition of the system in space. All vertices (nodes) and connections (arcs, edges) exist in these structures simultaneously (not separated in time).

Hierarchical structures in which each element of the lower level is subordinate to one node (one vertex) of the higher one (and this is true for all levels of the hierarchy) are called treelike structures (structures type "tree"; structures on which tree-order relations hold, hierarchical structures with strong connections) (Fig. 14, a).

Structures in which an element of a lower level can be subordinated to two or more nodes (vertices) of a higher level are called hierarchical structures with weak connections (Fig. 14, b).

In the form of hierarchical structures, the designs of complex technical products and complexes, the structures of classifiers and dictionaries, the structures of goals and functions, production structures, and organizational structures of enterprises are presented.

In general, the termhierarchy more broadly, it means subordination, the order of subordination of the lowest in position and rank of persons to the highest, arose as the name of the "service ladder" in religion, is widely used to characterize relationships in the apparatus of government, the army, etc., then the concept of hierarchy was extended to any coordinated subordination order of objects.

Thus, in hierarchical structures, only the allocation of levels of subordination is important, and there can be any relationship between levels and components within a level. In accordance with this, there are structures that use the hierarchical principle, but have specific features, and it is advisable to highlight them separately.

Often a situation arises when the elements of the system already exist, but the system as a whole does not yet exist.

A common mistake in this case is the further improvement of individual elements, and not building a system out of them. In the framework of TRIZ, in this case they say that the system is incomplete and it needs to be “finished” to get the desired system property / quality ...

So, the bullfighter and the bull separately do not form system. But the bullfighter, persistently waving a red rag in front of the bull, will obviously soon form a system ...

Here are two more characteristic examples from the history of aviation:

EXAMPLE.“...until the moment when all the knowledge necessary for innovation, on which they are based, does not come together, innovation will not become a reality, it will not take place. For example, Samuel Langley, who, according to the expectations of his contemporaries, was to become the inventor of the airplane, was much better prepared than Wright brothers. Secretary of the then leading scientific institution, the Smithsonian Institution in Washington, he had at his disposal all the scientific resources of the nation. But he preferred to ignore the gasoline engine, which had already been invented by that time. He believed in the steam engine. As a result, his airplane could take off; but due to the great weight of the steam engine, he could not take on board any cargo, not even a pilot. In order for an airplane to appear, a fusion of mathematics and a gasoline engine was required. Until all the necessary knowledge is merged together, the countdown to the time required for the innovation based on this new knowledge to become a reality does not even begin.”

In this article, we will consider the definition of a system as a device made up of various structural elements. Here the question of the classification of systems and their characteristics will be touched upon, as well as the formulation of Ashby's law and the concept of a general theory.

Introduction

The definition of a system is a multiple series of elements that are in a certain connection with each other and form an integrity.

The use of the system as a term is conditioned by the need to emphasize the various characteristics of something. As a rule, we are talking about a complex and huge structure of an object. It is most often difficult to disassemble such a mechanism unambiguously, which is another reason for using the term “system”.

The definition of a system has a characteristic difference from “set” or “collection”, which manifests itself in the fact that the main term of the article tells us about the order and integrity in a particular object. The system always has a certain pattern of its construction and functioning, and it also has the specifics of development.

Definition of the term

There are various definitions of the system, which can be classified according to a wide variety of characteristics. This is a very broad concept that can be used in relation to almost everything and in any science. The content of the context about the system, the field of knowledge and the purpose of study and analysis also strongly influence the definition of this concept. The problem of exhaustive characterization lies in the use of the term both objective and subjective.

Consider some descriptive definitions:

A system is a complex formation of interacting fragments of an integral "mechanism".
A system is a general accumulation of elements that are in some relation to each other, and also connected with the environment.
A system is a set of interconnected components and details, isolated from the environment, but interacting with it and working as a whole.

The first definitions of a system of a descriptive nature date back to the early period of the development of systems science. Such terminology included only elements and a set of links. Further, they began to include various concepts, for example, functions.

The system in everyday life

A person uses the definition of a system in various spheres of life and activity:

When naming theories, for example, the philosophical system of Plato.
When creating a classification.
When creating a structure.
When naming a set of established life norms and behavioral rules. An example is the system of legislation or moral values.

Systems research is a development in science that is studied in a wide variety of disciplines, such as engineering, systems theory, systems analysis, system science, thermodynamics, system dynamics, etc.

Characterization of a system by means of its constituent components

The main definitions of the system include a number of characteristics, through the analysis of which one can somehow give it an exhaustive description. Consider the main ones:

The limit of dividing the system into fragments is the definition of the element. From the point of view of the aspects under consideration, the tasks to be solved and the goal set, they can be classified and differed in different ways.
A component is a subsystem that is presented to us as a relatively independent particle of the system and at the same time possesses some of its properties and subgoal.
Communication is the relationship between the elements of the system and what they limit. Communication allows to reduce the degree of freedom of fragments of the "mechanism", but at the same time acquire new properties.
Structure - a list of the most significant components and relationships that change little during the current functioning of the system. She is responsible for the presence of the main properties.
The main concept in the definition of the system is also the concept of purpose. The goal is a multifaceted concept that can be defined depending on the data of the context and the stage of cognition at which the system is located.

The approach to defining a system also depends on concepts such as state, behavior, development, and life cycle.

Presence of patterns

When analyzing the main term of the article, it will be important to pay attention to the presence of some regularities. The first is the presence of limitations from the general environment. In other words, it is integrativity, which defines the system as an abstract entity that has integrity and clearly defined boundaries of its boundaries.

The system has synergy, emergence and holism, as well as a systemic and super-additive effect. Elements of the system may be interconnected between specific components, and with some they may not interact in any way, but the influence in any case turns out to be all-encompassing. It is produced through indirect interaction.

System definition is a term closely related to the phenomenon of hierarchy, which is the definition of the various parts of a system as separate systems.

Classification data

Almost all publications studying systems theory and systems analysis are discussing the question of how to properly classify them. The greatest diversity among the list of opinions about such a distinction concerns the definition of complex systems. The predominant part of the classifications refers to arbitrary, which are also called empirical. This means that most often the authors arbitrarily use this term in case of a need to characterize a certain problem being solved. The distinction is most often made by the definition of the subject and the categorical principle.

Among the main properties most often pay attention to:

The quantitative value of all components of the system, namely, monocomponent or multicomponent.
When considering a static structure, it is necessary to take into account the state of relative rest and the presence of dynamism.
Relation to closed or open type.
Characteristics of a deterministic system at a particular point in time.
It is necessary to take into account homogeneity (for example, a population of organisms in a species) or heterogeneity (the presence of different elements with different properties).
When analyzing a discrete system, regularities and processes are always clearly limited, and in accordance with the origin, they distinguish: artificial, natural and mixed.
It is important to pay attention to the degree of organization.

The definition of a system, types of systems and the system as a whole is also connected with the question of their perception as complex or simple. However, here there is the greatest number of disagreements when trying to give an exhaustive list of characteristics, according to which it is necessary to distinguish between them.

The concept of a probabilistic and deterministic system

The definition of the term "system" created and proposed by Art. Beer, has become one of the most widely known and widespread throughout the world. He put a combination of levels of determinism and complexity into the foundation of the difference, and received probabilistic and deterministic ones. Examples of the latter are simple structures such as window shutters and machine shop designs. The complex ones are represented by computers and automation.

A probabilistic device of elements in a simple form can be a coin toss, a jellyfish movement, the presence of statistical control in relation to product quality. Among the complex examples of a system, we can recall the storage of reserves, conditioned reflexes, etc. Super-complex forms of a probabilistic type: the concept of the economy, the structure of the brain, the firm, etc.

Ashby's Law

The definition of the concept of a system is closely related to Ashby's law. In the case of creating a certain structure in which the components have relationships with each other, it is necessary to determine the presence of a problem-solving ability. It is important that the system has a variety that exceeds the same indicator for the problem that is being worked on. The second feature is the ability of the system to create such diversity. In other words, the structure of the system must be regulated so that it can change its properties in response to a change in the conditions of the problem being solved or the manifestation of a disturbance.

In the absence of such characteristics in the phenomenon under study, the system will not be able to meet the requirements for management tasks. It will become ineffective. It is also important to pay attention to the presence of diversity in the list of subsystems.

The concept of a general theory

The definition of a system is not only its general characteristic, but also a set of various important aspects. One of them is the concept of the general theory of systems, which is presented in the form of a scientific and methodological concept of studying the objects that form the system. It is interconnected with such a terminological unit as "system approach", and is a list of its specified principles and methodologies. The first form of the general theory was put forward by L. von Bertalanffy, and his idea was based on the recognition of the isomorphism of the fundamental statements responsible for the control and functionality of the system objects.

1. Basic concepts of systems theory (definition of a system, environment, object, element; system of representations)

System - this is a complete, integral set of elements (components), interconnected and interacting with each other so that the function of the system can be realized.

The study of an object as a system involves the usea number of representation systems (categories), among which the main ones are:

Structural representation is associated with the selection of the elements of the system and the links between them.

Functional representation of systems - the allocation of a set of functions (purposeful actions) of the system and its components aimed at achieving a specific goal.

Macroscopic representation - understanding of the system as an indivisible whole, interacting with the external environment.

The microscopic representation is based on the consideration of the system as a set of interrelated elements. It involves the disclosure of the structure of the system.

The hierarchical representation is based on the concept of a subsystem, obtained by decomposing (decomposing) a system that has system properties that should be distinguished from its element - indivisible into smaller parts (from the point of view of the problem being solved). The system can be represented as a set of subsystems of different levels, constituting a system hierarchy, which is closed from below only by elements.

The procedural representation involves the understanding of a system object as a dynamic object, characterized by a sequence of its states in time.

object knowledge is the honor of the real world, which stands out and is perceived as a whole for a long time. An object can be material or abstract, natural or artificial. An object has an infinite set of properties. But in practice, we need a limited set of properties that are important to us.

External environment - The concept of "system" arises where and when we materially or speculatively draw a closed boundary between an unlimited or some limited set of elements. Those elements with their respective mutual conditioning that fall inside form a system.

Those elements that remained outside the boundary form a set, called in systems theory "system environment" or simply "environment", or "external environment".

It follows from these considerations that it is unthinkable to consider a system without its external environment. The system forms and manifests its properties in the process of interaction with the environment, while being the leading component of this impact.

Depending on the impact on the environment and the nature of interaction with other systems, the functions of systems can be arranged in ascending rank as follows:

passive existence;

material for other systems;

maintenance of higher order systems;

opposition to other systems (survival);

absorption of other systems (expansion);

transformation of other systems and environments (active role).

Any system can be considered, on the one hand, as a subsystem of a higher order (supersystem), and on the other hand, as a supersystem of a system of a lower order (subsystem). For example, the system "production shop" is included as a subsystem in a system of a higher rank - "firm". In turn, the "firm" supersystem can be a "corporation" subsystem.

Usually, more or less independent parts of systems appear as subsystems, distinguished according to certain characteristics, possessing relative independence, a certain degree of freedom.

Component - any part of the system that enters into certain relations with other parts (subsystems, elements).

Element with A system is a part of a system with uniquely defined properties that perform certain functions and are not subject to further division within the framework of the problem being solved (from the point of view of the researcher).

The concepts of element, subsystem, system are mutually transformable, the system can be considered as an element of a system of a higher order (metasystem), and an element, in in-depth analysis, as a system. The fact that any subsystem is simultaneously and relatively independent system leads to 2 aspects of the study of systems: at the macro- and micro-levels.

When studying at the macro level, the main attention is paid to the interaction of the system with the external environment. Moreover, higher-level systems can be considered as part of the external environment. With this approach, the main factors are the target function of the system (goal), the conditions for its functioning. At the same time, the elements of the system are studied from the point of view of their organization into a single whole, the impact on the functions of the system as a whole.

At the micro level, the internal characteristics of the system, the nature of the interaction of elements among themselves, their properties and operating conditions become the main ones.

Both components are combined to study the system.

2. Concepts of system structure. Links and their types.

The structure of the system is understood as a stable set of relations that remains unchanged for a long time, at least during the observation interval. The structure of the system is ahead of a certain level of complexity in terms of the composition of relations on the set of elements of the system, or equivalently, the level of diversity of the manifestations of the object.

Links are elements that carry out direct interaction between elements (or subsystems) of the system, as well as with elements and subsystems of the environment.

Communication is one of the fundamental concepts in the systems approach. The system as a whole exists precisely due to the presence of connections between its elements, i.e., in other words, the connections express the laws of the system's functioning. Relations are distinguished by the nature of the relationship as direct and reverse, and by the type of manifestation (description) as deterministic and probabilistic.

Direct connections are intended for a given functional transfer of matter, energy, information or their combinations - from one element to another in the direction of the main process.

feedback, basically, they perform informing functions, reflecting a change in the state of the system as a result of a control action on it. The discovery of the feedback principle was an outstanding event in the development of technology and had extremely important consequences. The processes of management, adaptation, self-regulation, self-organization, development are impossible without the use of feedback.

Rice. - Feedback example

With the help of feedback, the signal (information) from the output of the system (control object) is transmitted to the control body. Here, this signal, containing information about the work performed by the control object, is compared with a signal that specifies the content and amount of work (for example, a plan). In the event of a discrepancy between the actual and planned state of work, measures are taken to eliminate it.

The main feedback functions are:

counteracting what the system itself does when it goes beyond the established limits (for example, responding to quality degradation);

compensation of disturbances and maintenance of a state of stable equilibrium of the system (for example, equipment malfunctions);

synthesizing external and internal disturbances that seek to bring the system out of a state of stable equilibrium, reducing these disturbances to deviations of one or more controlled variables (for example, the development of control commands for the simultaneous appearance of a new competitor and a decrease in the quality of products);

development of control actions on the control object according to a poorly formalized law. For example, the establishment of a higher price for energy carriers causes complex changes in the activities of various organizations, changes the final results of their functioning, requires changes in the production and economic process through impacts that cannot be described using analytical expressions.

Violation of feedback in socio-economic systems for various reasons leads to serious consequences. Separate local systems lose the ability to evolve and perceive emerging new trends, long-term development and scientifically based forecasting of their activities for a long period of time, effective adaptation to constantly changing environmental conditions.

A feature of socio-economic systems is the fact that it is not always possible to clearly express the feedback, which in them, as a rule, is long, passes through a number of intermediate links, and it is difficult to see them clearly. The controlled variables themselves often do not lend themselves to a clear definition, and it is difficult to establish many restrictions on the parameters of the controlled variables. The real reasons for the controlled variables to go beyond the established limits are also not always known.

Deterministic (hard) connection, as a rule, uniquely determines the cause and effect, gives a clearly defined formula for the interaction of elements.Probabilistic (flexible) connection -Defines an implicit and indirect dependency between elements. Probability theory offers a special mathematical apparatus for the study of these relationships, called correlation analysis.

Criteria are signs by which the conformity of the functioning of the system to its purpose is assessed under given restrictions

The efficiency of the system is the ratio between the target result of functioning and the actually realized one.

Often there are restrictions on the input and output - provides a correspondence between the output of the system and the requirements for entry into the subsequent system. If the requirements are not met, the restriction does not allow it to pass through itself, that is, it works on the principle of a filter.

The state of the system is a set of essential properties that the system has at the current moment.

3. Basic properties of systems. (6 properties).

A property is understood as the side of an object (its characteristic), which determines its difference or similarity with another object, or manifests itself during interaction.

It follows from the definition of the system that the main property is the integrity or unity provided by the relationships between the components and manifested in the emergence of new properties that individual elements do not possess.

This property is called the emergence property.

Emergence - a property of systems that causes the emergence of new properties and qualities that are not inherent in individual elements of the system. It is based on the principle opposite to reductionism, which states that the whole can be studied by dividing it into parts and then, having determined the properties of the parts, determine the properties of the whole.

Integrity - each element of the system contributes to the realization of the goal of the system.

Integrity and emergence are the integrative properties of the system.

Integrity lies in the fact that each of the components provides its own pattern of functionality and goal achievement.

The presence of integrative properties is one of the most important features of the system. Integrity is manifested in the fact that the system has its own pattern of functionality, its own purpose.

organization- a complex property of systems, consisting in the presence of structure and functioning (behavior). The indispensable property of systems is their components, namely those structural formations that make up the whole and without which it is not possible.

Functionality- this is a manifestation of certain properties (functions) when interacting with the external environment. Here, the goal (purpose of the system) is defined as the desired end result.

Structurality - this is the ordering of the system, a certain set and arrangement of elements with links between them. There is a relationship between the function and structure of the system, as between the philosophical categories of content and form. A change in content (functions) entails a change in form (structure), but vice versa.

An important property of the system is the presence of behavior- actions, changes, functioning, etc. It is believed that this behavior of the system is associated with the environment (environment), i.e. with other systems with which it comes into contact or enters into certain relationships. The process of purposeful change in time of the state of the system is called behavior. Unlike control, when a change in the state of the system is achieved due to external influences, behavior is implemented exclusively by the system itself, based on its own goals.

Another property is the property of growth (development). Development can be seen as an integral part of behavior (and the most important).

The fundamental property of systems is stability, i.e. the ability of the system to withstand external disturbing influences. It affects the lifespan of the system. Simple systems have passive forms of stability: strength, balance, controllability, homeostasis. And for complex ones, active forms are decisive: reliability, survivability and adaptability. If the listed forms of stability of simple systems (except for strength) concern their behavior, then the determining form of stability of complex systems is mainly structural in nature.

Reliability - the property of preserving the structure of systems, despite the death of its individual elements by replacing or duplicating them, and survivability - as an active suppression of harmful qualities. Thus, reliability is a more passive form than survivability.

Adaptability - the ability to change behavior or structure in order to maintain, improve or acquire new qualities in a changing environment. A prerequisite for the possibility of adaptation is the presence of feedback.

4. Classification of systems by content. Give a brief description of each class.

classification is called the division into classes according to the most significant features. Under class is understood as a set of objects that have some features of generality. A sign (or a set of signs) is the basis (criterion) of classification.

A system can be characterized by one or more features and, accordingly, it can be placed in various classifications, each of which can be useful in choosing a research methodology. Usually the goal of classification is to limit the choice of approaches to displaying systems, to develop a description language suitable for the corresponding class.

Real Systemsare divided into natural (natural systems) and artificial (anthropogenic).

natural systems: systems of inanimate (physical, chemical) and living (biological) nature.

Artificial systems:are created by mankind for their needs or are formed as a result of purposeful efforts. artificialare divided into technical (techno-economic) and social (public).A technical system is designed and manufactured by a person for specific purposes.

TO social systemsinclude various systems of human society.

The selection of systems consisting of only technical devices is almost always conditional, since they are not capable of generating their own state. These systems act as parts of larger, including people - organizational and technical systems.

An organizational system, for the effective functioning of which an essential factor is the way of organizing the interaction of people with a technical subsystem, is calledman-machine system. Examples of man-machine systems: car - driver; aircraft - pilot; COMPUTER - user, etc.

Thus, undertechnical systemsunderstand a single constructive set of interconnected and interacting objects, intended for purposeful actions with the task of achieving a given result in the process of functioning. The distinguishing features of technical systems in comparison with an arbitrary set of objects or in comparison with individual elements are constructiveness (practical feasibility of relations between elements), orientation and interconnectedness of constituent elements and purposefulness.

In order for the system to be resistant to external influences, it must have a stable structure. The choice of structure practically determines the technical appearance of both the entire system and its subsystems and elements. The question of the appropriateness of using a particular structure should be decided on the basis of the specific purpose of the system. The structure also determines the ability of the system to redistribute functions in the event of a complete or partial withdrawal of individual elements, and, consequently, the reliability and survivability of the system for given characteristics of its elements.

Abstract systemsare the result of the reflection of reality (real systems) in the human brain. Their mood is a necessary step in ensuring effective human interaction with the outside world. Abstract (ideal) systems are objective in terms of their source of origin, since their primary source is an objectively existing reality.
Abstract systems divideon direct display systems(reflecting certain aspects of real systems)and systems of generalizing (generalizing) mapping.The former include mathematical and heuristic models, while the latter include conceptual systems (theories of methodological construction) and languages.

5. Classification of systems into 9 groups. Give a brief description of each class.

open called a system interacting with the environment. All real systems are open. When describing the structure of such systems, external communication channels are tried to be divided into input and output.

In an open system, at least 1 element has a connection with the external environment.

In a real system, the number of interconnections is enormous. Therefore, one of the researcher's tasks is to single out and include only significant links in the system. Irrelevant are discarded.

closed system- one that does not interact with the environment, or interacts with it in a strictly defined way. In the second case, there are input channels, but the impact of the environment is unchanged and fully known in advance. In this case, such impacts are attributed directly to the system, which allows us to consider it as a closed one.

Combined systemscontain open and closed subsystems. That is, one or more subsystems can be distinguished in them, interacting with the environment, and the remaining subsystems are closed.

Simple Systems - do not have branched structures and consist of a small number of relationships and elements. It serves to perform the simplest functions; it is impossible to single out hierarchical levels in them. A distinctive feature is the determinism (clear certainty) of the nomenclature, the number of elements and internal and external links.

Complex - contain a large number of elements and internal connections, differ in structural diversity. Performs a complex function or a series of functions. Can be easily divided into subsystems. A system is called complex if its knowledge requires the involvement of several scientific disciplines, theories, models, as well as accounting for uncertainty.

A model is a kind of description (mathematical, verbal, etc.) of a system or subsystem that reflects a group and its property.

A system is said to be complex if, in reality, the following signs of complexity are essentially manifested:

Structural complexity

Basic concepts of relationships:

Structural

Hierarchical

Functional

Causal (causal)

Informational

Spatio-temporal

Complexity of functioning (behavior)

Complexity of behavior choice. In multi-alternative situations, the choice of behavior is determined by the purpose of the system.

Complexity of development.

It is determined by the characteristics of evolutionary or stochastic processes.

These features should be considered in conjunction. Complex systems are characterized by weak predictability, secrecy, and a variety of possible states.

big systemcalled a system that cannot be observed simultaneously from the position of one observer in time and space. That is, the spatial factor is essential for it. The number of its subsystems is very large, and the composition is heterogeneous. In the analysis and synthesis of large and complex systems, decomposition and aggregation procedures are fundamental.

For specialized systemsthe uniqueness of the appointment and the narrow specialization of the service personnel are characteristic. In universal systems, many actions are also performed on a single structure, however, the composition of functions in terms of their type and number is less homogeneous.

Automatic - uniquely respond to a limited set of external interactions. The internal organization has several equilibrium states.

Decisive - have constant criteria for distinguishing external influences and constant reactions to them.

self-organizing- have flexible criteria for distinguishing and flexible reactions to external influences. Can adapt to influences. They have signs of diffuse systems, stochastic behavior and instability of parameters and processes. Able to slightly change the structure. For example: biological organizations, collective behavior of people, etc. If it surpasses external influences in its stability, thenthese are predictive systems. That is, they can foresee the further course of events.

Transforming systems- imaginary complex systems at the highest level of complexity, not bound by the persistence of existing carriers. They can change material carriers and their structure, while maintaining their individuality.

They are called deterministicsystems for which their state is uniquely determined by the initial moment and can be predicted for any subsequent moment in time.Stochastic systems- systems in which changes are random. In this case, the initial data for prediction is not enough.

A system is called centralized if one of its parts has a dominant (central) role, which determines the functioning.

decentralizedsystems are those systems in which the components are equally significant.

In producing systems, processes for obtaining products or services are implemented. Such systems are divided into material-energy and information.

Control systems- are engaged in the organization and management of material-energy and information processes.

Service systems- support the performance of production and control systems.

6. Name the patterns of interaction between the part and the whole (2). Give a brief description of each pattern.

Progressive systematization

d > B

Progressive factorization

Additivity (summativity)

The regularity of integrity/emergence is manifested in the system in the appearance of new properties in it that are absent from the elements. In order to better understand the regularity of integrity, it is necessary, first of all, to take into account its two sides:

properties of the (whole) system Qs is not a simple sum of the properties of its constituent elements (parts):

Qs ≠ ∑Qi

the properties of the system (whole) depend on the properties of its constituent elements (parts):

Qs = f(qi)

In addition to these two main aspects, it should be borne in mind that the elements combined into a system, as a rule, lose some of their properties that are inherent in them outside the system, i.e. the system, as it were, suppresses a number of properties of elements. But, on the other hand, once elements enter the system, they can acquire new properties.

Let us turn to the pattern dual in relation to the pattern of integrity. It is called physical additivity, independence, summativity, isolation. The property of physical additivity is manifested in the system, as if broken up into independent elements; then it becomes fair

Qs = ∑Qi

In this extreme case, it is no longer possible to speak of a system.

Consider intermediate options - two conjugate patterns that can be called progressive factorization - the desire of the system to a state with more and more independent elements, and progressive systematization - the desire of the system to reduce the independence of elements, i.e. to greater integrity.

Integrity - This term is often used as a synonym for integrity. However, some researchers single out this regularity as an independent one, trying to emphasize the interest not in external factors of manifestation of integrity, but in deeper causes that cause the emergence of this property, to factors that ensure the preservation of integrity.

System-forming, system-preserving factors are called integrative, among which an important role is played by the heterogeneity and inconsistency of elements (explored by most philosophers), on the one hand, and their desire to join coalitions, on the other.

7. Name the patterns of hierarchical ordering (2). Give a brief description of each pattern.

This group of regularities also characterizes the interaction of the system with its environment - with the environment (significant or essential for the system), supersystem, subordinate systems.

Communication- This regularity forms the basis for the definition of a system, where the system is not isolated from other systems, it is connected by many communications with the environment, which, in turn, is a complex and heterogeneous formation containing a supersystem (a metasystem is a higher-order system that sets the requirements and limitations of the studied system), subsystems (underlying, subordinate systems), and systems of the same level as the one under consideration.

Such a complex unity with the environment is called the pattern of communication, which, in turn, easily helps to move to hierarchy as a pattern of building the whole world and any system separated from it.

Hierarchy - The laws of hierarchy or hierarchical ordering were among the first laws of systems theory that L. fon singled out and studied. Bertalanffy. It is necessary to take into account not only the external structural side of the hierarchy, but also the functional relationships between levels. For example, in biological organizations, a higher hierarchical level has a guiding effect on the lower level subordinate to it, and this effect is manifested in the fact that the subordinate members of the hierarchy acquire new properties that they did not have in an isolated state (confirmation of the position on the influence of the whole on the elements given above), and as a result of the appearance of these new properties, a new, different “image of the whole” is formed (the influence of the properties of elements on the whole). The new whole that has arisen in this way acquires the ability to perform new functions, which is the purpose of the formation of hierarchies.

The main features of hierarchical ordering are:

Direct interaction of the system with higher and lower levels. In this case, the concept of a supersystem and a subsystem appears, a goal for the general level (for high levels), a subgoal (for low and medium levels) and a means (for underlying ones)

The pattern of integrity and emergence manifests itself at each level of the hierarchy.

8. Name the patterns of systems feasibility. Give a brief description of each pattern.

The problem of system feasibility is the least explored. Let us consider some of the patterns that help to understand this problem and take it into account when determining the principles for designing and organizing the functioning of control systems.

equifinality- This pattern characterizes, as it were, the limiting capabilities of the system. L. von Bertalanffy, who proposed this term, defined equifinality as “the ability, in contrast to the equilibrium state in closed systems, completely determined by the initial conditions, ... to achieve a time-independent state that does not depend on its initial conditions and is determined solely by the parameters of the system ". In accordance with this pattern, the system can reach the required final state, which is independent of time and determined solely by the system's own characteristics under different initial conditions and in different ways. This is a form of stability with respect to initial and boundary conditions.

The law of "necessary variety" -W.R. Ashby. He formulated a pattern known as the law of "necessary variety". For decision-making problems, the most important is one of the consequences of this pattern, which can be simplified in the following example.

When a researcher (DM - decision maker, observer) N encounters a problem D, the solution of which is not obvious to him, then there is a certain variety of possible solutions Vd. This diversity is opposed by the diversity of thoughts of the researcher (observer) Vn. The task of the researcher is to reduce the diversity Vd - Vn to a minimum, ideally to 0.

Ashby proved a theorem on the basis of which the following conclusion is formulated: “If Vd is given a constant value, then Vd - Vn can only be reduced by a corresponding increase in Vn. only variety in N can reduce the variety created in D; only diversity can destroy diversity.”

As applied to control systems, the law of “required diversity” can be formulated as follows: the diversity of the control system (control system) Vsu must be greater than (or at least equal to) the diversity of the managed object Vou:

Vsu > Vou.

The following ways of improving management with increasing complexity of production processes are possible:

an increase in Vsu, which can be achieved by increasing the number of the administrative apparatus, improving its qualifications, mechanizing and automating managerial work;

reduction of Vou, due to the establishment of clearer and more specific rules for the behavior of system components: unification, standardization, typification, the introduction of in-line production, a reduction in the range of parts, assemblies, technological equipment, etc.;

reducing the level of management requirements, i.e. reduction in the number of constantly monitored and adjustable parameters of the controlled system;

self-organization of control objects by limiting controlled parameters by creating self-regulating units (workshops, sites with a closed production cycle, with relative independence and limiting the intervention of centralized enterprise management bodies, etc.).

9. Name the patterns of development of systems (2). Give a brief description of each pattern.

Recently, the need to take into account, when modeling systems, the principles of their change in time, is becoming more and more recognized, for understanding which the regularities considered below can help.

Historicity - Although it would seem obvious that any system cannot be unchanged, that it not only arises, functions, develops, but also dies, and everyone can easily give examples of formation, flourishing, decline (aging) and even death (death) biological and social systems, yet for specific cases of the development of organizational systems and complex technical complexes it is difficult to determine these periods. The heads of organizations and designers of technical systems do not always take into account that time is an indispensable characteristic of the system, that each system is subject to the laws of historicity, and that this pattern is as objective as integrity, hierarchical order, etc. At the same time, the pattern of historicity can be taken into account not only passively , fixing aging, but also used to prevent the "death" of the system, developing "mechanisms" for reconstruction, reorganization of the system to preserve it in a new quality.

The pattern of self-organization-Among the main features of self-organizing systems with active elements are the ability to resist entropy (entropy in this case is the degree of uncertainty, unpredictability of the state of the system and the environment) tendencies, the ability to adapt to changing conditions, transforming its structure if necessary, etc. These outwardly manifesting abilities are based on a deeper pattern based on the combination of two conflicting trends in any real developing system: on the one hand, for all phenomena, including developing, open systems, the second law of thermodynamics is valid (“second law”) , i.e. the desire to increase entropy; on the other hand, there are negentropic (opposite to entropic) tendencies underlying evolution.

Important results in understanding the patterns of self-organization have been obtained in studies that are classified as a developing science called synergetics.

10. What is synergy? What is it for? Give a brief description of the 9 main principles of the synergistic approach.

Synergetics is an interdisciplinary scientific direction that studies the universal laws of the processes of self-organization, evolution and cooperation. Its purpose is to construct a general theory of complex systems with special properties. Unlike simple systems, complex systems have the following main characteristics:

many heterogeneous components;

activity (purposefulness) of components;

many different, parallel relationships between components;

semiotic (weakly formalizable) nature of relationships;

cooperative behavior of components;

openness;

distribution;

dynamism, learning ability, evolutionary potential;

uncertainty of environment parameters.

A special place in synergetics is occupied by questions of spontaneous formation of ordered structures of various nature in interaction processes when the initial systems are in unstable states. Following the scientist I.Prigozhin, it can be briefly described as a "complex of sciences about emerging systems."

According to synergetic models, the evolution of a system is reduced to a sequence of nonequilibrium phase transitions. The principle of development is formulated as a successive passage of critical areas (points of bifurcations (bifurcations, ramifications)). Near the bifurcation points, there is a sharp increase in fluctuation (from Latin fluctuatio - fluctuation, deviation). The choice of development after the bifurcation is determined at the moment of instability. Therefore, the bifurcation zone is characterized by fundamental unpredictability - it is not known whether the further development of the system will become chaotic or a new, more ordered structure will be born. Here the role of uncertainty sharply increases: randomness at the entrance to a non-equilibrium situation can have catastrophic consequences at the exit. At the same time, the very possibility of spontaneous emergence of order from chaos is the most important moment of the process of self-organization in a complex system.

The main principles of the synergetic approach in modern science are as follows:

Complementarity principle of N. Bohr.In complex systems, there is a need to combine different models and methods of description that previously seemed incompatible, but now complementary to each other.

The principle of spontaneous emergence by I. Prigogine. In complex systems, special critical states are possible, when the slightest fluctuations can suddenly lead to the emergence of new structures that are completely different from the usual ones (in particular, this can lead to catastrophic consequences - “snowball” or epidemic effects).

Principle of incompatibility L. Zadeh. With an increase in the complexity of the system, the possibility of its accurate description decreases up to a certain threshold, beyond which the accuracy and relevance (semantic coherence) of information become incompatible, mutually exclusive characteristics.

The principle of uncertainty management.In complex systems, a transition from dealing with uncertainties to managing uncertainties is required. Various types of uncertainty should be deliberately introduced into the model of the system under study, since they serve as a factor that favors innovation (system mutations).

Principle of ignorance. Knowledge about complex systems is fundamentally incomplete, inaccurate and contradictory: it is usually formed not on the basis of logically rigorous concepts and judgments, but on the basis of individual opinions and collective ideas. Therefore, modeling of partial knowledge and ignorance plays an important role in such systems.

Conformity principle. The language for describing a complex system must correspond to the nature of the information available about it (the level of knowledge or uncertainty). Exact logical-mathematical, syntactic models are not a universal language; non-strict, approximate, semiotic models and informal methods are also important. One and the same object can be described by a family of languages of different rigidity.

The principle of diversity of development paths. The development of a complex system is multivariate and alternative, there is a "spectrum" of ways of its evolution. The critical turning point of the uncertainty of the future development of a complex system is associated with the presence of bifurcation zones - "branching" of possible paths for the evolution of the system.

The principle of unity and mutual transitions of order and chaos. The evolution of a complex system goes through instability; Chaos is not only destructive, but also constructive. The organizational development of complex systems involves a kind of conjunction of order and chaos.

The principle of oscillatory(pulsating) evolution. The process of evolution of a complex system is not progressive, but cyclic or wave in nature: it combines divergent (increase in diversity) and convergent (folding in diversity) trends, phases of the birth of order and maintenance of order. Open complex systems pulsate: differentiation is replaced by integration, scatter - by rapprochement, weakening of ties - by their strengthening, etc.

It is easy to understand that the listed principles of synergetic methodology can be divided into three groups: the principles of complexity (1-3), the principles of uncertainty (3-6) and the principles of evolution (7-9).

11. What are the patterns of emergence and formulation of goals (4). Give a brief description of each pattern.

Generalization of the results of studies of goal formation processes conducted by philosophers, psychologists, cybernetics, and observation of the processes of substantiation and structuring of goals in specific conditions made it possible to formulate some general principles, patterns that are useful to use in practice.

The dependence of the idea of the goal and the formulation of the goal on the stage of cognition of the object (process) and on time -An analysis of the definitions of the concept of "goal" allows us to conclude that, when formulating the goal, one should strive to reflect in the formulation or in the way of presenting the goal the main contradiction: its active role in cognition, in management, and at the same time the need to make it realistic, to direct with the help of activities to obtain a certain useful result. At the same time, the formulation of the goal and the idea of the goal depend on the stage of cognition of the object, and as the idea of it develops, the goal can be reformulated.

The dependence of the goal on external and internal factors- When analyzing the causes of the emergence and formulation of goals, it should be taken into account that the goal is influenced by both external factors in relation to the system (external requirements, needs, motives, programs) and internal factors (needs, motives, programs of the system itself and its elements, performers goals); at the same time, the latter are the same factors that objectively influence the process of goal formation, as well as external factors (especially when using the concept of goal as a means of inducing action in management systems).

The manifestation in the structure of goals of the regularity of integrity -In a hierarchical structure, the regularity of integrity (emergence) manifests itself at any level of the hierarchy. In relation to the structure of goals, this means that, on the one hand, the achievement of a goal of a higher level cannot be fully ensured by the achievement of subgoals subordinate to it, although it depends on them, and, on the other hand, needs, programs (both external and internal) it is necessary to investigate at each level of structuring, and the divisions of subgoals obtained by different decision makers, due to different disclosures of uncertainty, may turn out to be different, i.e. different decision makers can offer different hierarchical structures of goals and functions, even when using the same structuring principles and techniques.

Patterns of formation of hierarchical structures of goals -Considering that the most common way to represent goals in organizational management systems are tree-like hierarchical structures ("goal trees"), let's consider the main recommendations for their formation:

the techniques used in the formation of tree-like hierarchies of goals can be reduced to two approaches: a) the formation of structures "from above" - methods of structuring, decomposition, target or goal-oriented approach, b) the formation of structures of goals "from below" - morphological, linguistic, thesaurus, terminal approach ; in practice, these approaches are usually combined;

the goals of the lower level of the hierarchy can be considered as a means to achieve the goals of the higher level, while they are also goals for the level below them;

in the hierarchical structure, as you move from the upper level to the lower one, there is a shift of the “scale” considered above from the goal-direction (goal-ideal, goal-dream) to specific goals and functions, which at the lower levels of the structure can be expressed in the form of expected results specific work, indicating the criteria for evaluating its performance, while at the upper levels of the hierarchy, the indication of criteria can either be expressed in general requirements (for example, “increase efficiency”), or not at all in the formulation of the goal;

in order for the structure of goals to be convenient for analysis and organization of management, it is recommended to impose some requirements on it - the number of hierarchy levels and the number of components in each node should be (due to the Miller hypothesis or the Kolmogorov number) K = 5 ± 2 (human perception limit) .

And a few more important laws.

Law of Simplicity of Complex Systems- It is realized, survives, the variant of a complex system that has the least complexity is selected. The law of simplicity of complex systems is realized by nature in a number of constructive principles:

occam,

hierarchical modular construction of complex systems,

symmetry,

symmorphosis (equal strength, uniformity),

field interaction (interaction through a carrier),

extreme uncertainty (distribution functions of characteristics and parameters that have uncertain values have extreme uncertainty).

The law of finiteness of the rate of propagation of interaction- All types of interaction between systems, their parts and elements have a finite propagation speed. The speed of changing the states of the elements of the system is also limited. The author of the law is A. Einstein.

Godel's incompleteness theorem- In sufficiently rich theories (including arithmetic), there are always unprovable true expressions. Since complex systems include (implement) elementary arithmetic, deadlock situations (freezes) may occur when performing calculations in it.

The law of equivalence of options for building complex systems- As the complexity of the system grows, the proportion of options for its construction that are close to the optimal option grows.

Onsager's law maximization of the entropy decrease - If the number of possible forms of the process implementation, consistent with the laws of physics, is not unique, then the form is realized in which the entropy of the system grows most slowly. In other words, the form is realized in which the decrease in entropy or the increase in information contained in the system is maximized.

12. What is meant by the functional description of systems? Why and how is it done? Explain the general formula for the functional description of any dynamical system.

The study of any system involves the creation of a system model that allows you to analyze and predict its behavior in a certain range of conditions, solve problems of analysis and synthesis of a real system. Depending on the goals and objectives of modeling, it can be carried out at various levels of abstraction.

A model is a description of a system that reflects a certain group of its properties.

It is advisable to start the description of the system from three points of view: functional, morphological and informational.

Any object is characterized by the results of its existence, the place it occupies among other objects, the role it plays in the environment. A functional description is necessary in order to realize the importance of the system, to determine its place, to evaluate the relationship with other systems.

A functional description (functional model) should create the correct orientation in relation to the external relations of the system, its contacts with the outside world, and the directions of its possible change.

The functional description proceeds from the fact that any system performs some functions: it simply passively exists, serves as a habitat for other systems, serves systems of a higher order, serves as a means for creating more perfect systems.

As we already know, the system can be single-functional and multifunctional.

In many ways, the evaluation of the functions of the system (in the absolute sense) depends on the point of view of the one who evaluates it (or the system that evaluates it).

The functioning of the system can be described by a numerical functional depending on the functions that describe the internal processes of the system, or by a qualitative functional (ordering in terms of "better", "worse", "more", "less", etc.)

The functional that quantitatively or qualitatively describes the activity of the system is called the efficiency functional.

The functional organization can be described as:

algorithmically,

analytically,

graphically,

tabular,

through timing diagrams of functioning,

verbally (wordly).

The description must correspond to the concept of development of systems of a certain class and meet certain requirements:

should be open and allow the possibility of expanding (narrowing) the range of functions implemented by the system;

provide for the possibility of moving from one level of consideration to another, i.e. ensure the construction of virtual models of systems of any level.

When describing a system, we will consider it as a structure into which something (substance, energy, information) is introduced at certain points in time, and from which something is output at certain points in time.

In the most general form, the functional description of a system in any dynamic system is represented by a seven:

Sf = (T, x, C, Q, y, φ, η),

where T is the set of time points, x is the set of instantaneous values of input actions, С = (c: T → x) is the set of admissible input actions; Q - set of states; y - set of output values; Y = (u: T → y) - set of output values; φ = (T×T×T×c → Q) - state transition function; η:T×Q → y - output mapping; c - segment of the input action; u - segment of the output value.

Such a description of the system covers a wide range of properties.

The disadvantage of this description is not constructiveness: the difficulty of interpretation and practical application. A functional description should reflect such characteristics of complex and poorly known systems as parameters, processes, hierarchy.

Let us assume that the system S performs N functions ψ1, ψ2, ..., ψs, ..., ψN, depending on n processes F1, F2, ..., Fi, ..., Fn. Efficiency of execution of the s-th function

Es = Es(ψs) = E(F1, F2, ..., Fi, ..., Fn) = Es((Fi)), i = 1...n, s = 1...N.

The overall efficiency of the system is the vector-functional E = (Es). The effectiveness of the system depends on a huge number of internal and external factors. It is extremely difficult to represent this dependence in an explicit form, and the practical value of such a representation is negligible due to the multidimensionality and multiply connectedness. A rational way to form a functional description is to use such a multi-level hierarchy of descriptions, in which the description of a higher level will depend on the generalized and factorized variables of the lower level.

The hierarchy is created by level factorization of processes (Fi) using generalized parameters (Qi), which are functionals (Fi). It is assumed that the number of parameters is much less than the number of variables on which the processes depend. This way of description allows building a bridge between the properties of the elements interacting with the environment (subsystems of the lower level) and the efficiency of the system.

Processes (Fi(1)) can be detected at the output of the system. These are the processes of interaction with the environment. We will call them processes of the first level and assume that they are defined:

first level system parameters - Q1(1), Q2(1), ..., Qj(1), ..., Qm(1);

active opposing parameters of the environment, directly directed against the system to reduce its effectiveness - b1, b2, ..., bk, ..., bK;

neutral (random environment parameters) c1, c2, ..., cl, ..., cL;

favorable environment parameters d1, d2, ..., dp, ..., dP.

The environment has direct contact with subsystems of lower levels, acting through them on subsystems of a higher level of the hierarchy, so that Fi* = Fi*((bk), (cl), (dp)). By constructing a hierarchy (parameters of the β-th level - processes of the (β-1)-th level - parameters of the (β-1)-th level), one can associate the properties of the environment with the efficiency of the system.

The system parameters (Qj) can change when the environment changes, they depend on the processes in the system and are written as state functionals Qj1(t).

The proper functional space of the system W is the space whose points are all possible states of the system, determined by the set of parameters up to level b:

Q = (Q(1), Q(2), ... Q(β)).

The state can be kept constant for some time interval T.

Processes (Fi(2)) cannot be detected at system output. These are the processes of the second level, which depend on the parameters Q(2) of the subsystems of the system (parameters of the second level). Etc.

The following description hierarchy is formed: efficiency (a finite set of functionals) - first-level processes (functions) - first-level parameters (functionals) - second-level processes (functions) - second-level parameters (functionals), etc. At some level, our knowledge of the functional properties of the system is exhausted, and the hierarchy breaks off. A break can occur at different levels for different parameters (processes), both on the process and on the parameter.

The external characteristics of the system are determined by the top level of the hierarchy, so it is often possible to confine ourselves to the description of the form ((Эi),(ψS), (Fi(1)), (Qj(1)), (bk), (cl), (dp)). The number of hierarchy levels depends on the required accuracy of input processes representation.

13. Graphical methods of functional description of systems. Tree of system functions.

The method of generalized analytical functional description of systems was considered above. Very often, in the analysis and synthesis of systems, a graphical description is used, the varieties of which are:

system function tree,

functional modeling standard IDEF0.

All functions implemented by a complex system can be conditionally divided into three groups:

objective function;

basic functions of the system;

additional features of the system.

The target function of the system corresponds to its main functional purpose, i.e. target (main) function - reflects the purpose, essence and meaning of the existence of the system.

The main functions reflect the orientation of the system and represent a set of macro functions implemented by the system. These functions determine the existence of a system of a certain class. Basic functions - provide conditions for the implementation of the target function (reception, transmission, acquisition, storage, issuance).

Additional (service) functions expand the functionality of the system, the scope of their application and improve the quality of the system. Additional functions - provide conditions for the implementation of basic functions (connection (breeding, direction, guarantee)).

The description of an object in the language of functions is represented as a graph.

The wording of the function inside the vertices should include 2 words: the verb and the noun "Do what".

The system functions tree represents a decomposition of the system functions and is formed for the purpose of a detailed study of the system functionality and analysis of the set of functions implemented at different levels of the system hierarchy. On the basis of the tree of system functions, the system structure is formed on the basis of functional modules. In the future, the structure based on such modules is covered by constructive modules (for technical systems) or organizational modules (for organizational and technical systems). Thus, the stage of forming the function tree is one of the most important not only in the analysis, but also in the synthesis of the system structure. Errors at this stage lead to the creation of "disabled systems" that are not capable of fully functional adaptation with other systems, the user and the environment.

The initial data for the formation of the function tree are the main and additional functions of the system.

The formation of a function tree represents the process of decomposition of the objective function and the set of basic and additional functions into more elementary functions implemented at subsequent levels of decomposition.

At the same time, each of the functions of a specifically taken i-th level can be considered as a macrofunction in relation to the functions that implement it at the (i+1)-th level, and as an elementary function in relation to the corresponding function of the upper (i-1)-th level.

The description of system functions using IDEF0 notation is based on the same decomposition principles, but is presented not as a tree, but as a set of diagrams.

14. Graphical methods of functional description of systems. IDEF0 methodology. The syntax of the language.

The objects of modeling are systems.

The description of the IDEF0 model is built in the form of a hierarchical pyramid, at the top of which is the most general description of the system, and the bottom is a set of more detailed descriptions.

IDEF0 methodology is built on the following principles:

Graphic description of the simulated processes. Graphical language of Blocks and Arcs IDEF0 Diagrams displays operations or functions in the form of Blocks, and the interaction between the inputs/outputs of operations entering or leaving the Block, Arcs.

Conciseness. Due to the use of a graphic language for describing processes, on the one hand, the accuracy of the description is achieved, and on the other, brevity.

The need to comply with the rules and the accuracy of information transfer. When modeling IDEF0, you must adhere to the following rules:

There must be at least 3 and no more than 6 functional Blocks on the Diagram.

Diagrams should display information within the context defined by purpose and point of view.

Diagrams must have a coherent interface when Block numbers, Arcs and ICOM codes have the same structure.

Uniqueness of block function names and arc names.

Clear definition of the role of data and separation of inputs and controls.

Notes for Arcs and Block function names should be short and concise.

Each Function Block requires at least one Control Arc.

A model is always built for a specific purpose and from a specific point of view.

In the process of modeling, it is very important to clearly define the direction of the development of the model - its context, point of view and purpose.

The context of the model outlines the boundaries of the system being modeled and describes its relationship with the external environment.

It must be remembered that one model represents one point of view. Multiple models are used to model a system from multiple perspectives.

The purpose reflects the reason for creating the model and determines its purpose. At the same time, all interactions in the model are considered precisely from the point of view of achieving the set goal.

Within the framework of the IDEF0 methodology, the system model is described using Graphic IDEF0 Diagrams and refined through the use of FEO, Text and Glossary Diagrams. At the same time, the model includes a series of interconnected Diagrams that divide a complex system into its component parts. Diagrams of a higher level (A-0, A0) - are the most general description of the system, presented in the form of separate Blocks. The decomposition of these Blocks makes it possible to achieve the required level of detail in the description of the system.

The development of IDEF0 Diagrams begins with the construction of the highest level of the hierarchy (A-0) - one Block and interface Arcs that describe the external links of the system under consideration. The name of the function, written in Block 0, is the target function of the system from the accepted point of view and the purpose of building the model.

In further modeling, Block 0 is decomposed on Diagram A0, where the objective function is refined using several Blocks, the interaction between which is described using Arcs. In turn, the functional Blocks in Diagram A0 can also be decomposed for a more detailed representation.

As a result, the names of functional Blocks and interface Arcs that describe the interaction of all Blocks presented in the Diagrams form a hierarchical mutually consistent model.

Although the top of the model is the A-0 Diagram, the real “working vertex or structure” is the A0 Diagram, since it is a refined expression of the model's point of view. Its content indicates what will be considered further, limiting the subsequent levels within the scope of the project goal. The lower levels specify the content of the functional Blocks, detailing them, but without expanding the boundaries of the model.

15. IDEF0 methodology. Doug concept. Five types of relationships between blocks. Block decomposition principle.

Blocks represent functions or actions of a system. Their actions are written verb + action object + object

for example, "develop a schedule of work."

Arcs display information or material objects that are necessary to perform a function or appear as a result of execution. The role of an object can be: Documents, physical materials, tools, machines, information, organizations and even subsystems. The connection point of the arc with the block determines the interface type. Remarks to the arc are formulated as a turnover of a noun, answering the question "what". Blocks are arranged on the diagram according to the degree of the author, depending on the degree of the author. The dominant block is the block whose execution affects the control for the maximum number of blocks. The dominant block is located in the upper left corner, the least important - in the lower right.

Important!

The location of the blocks does not set the time dependence of the operation!

See fig. one

Relationship management.

Input relationship. (conveyor)

Management feedback. The output of the first function controls the input of the second, which in turn affects the operation of the first.

Input feedback.

Relationship output - mechanism. A rare type of communication used in preparatory operations.

Example: create an idef model for the control department to evaluate the effectiveness of the management and functioning of the library. see Figure 2. Block A0, reflecting the objective function. Then, in Figure 3, the diagram A0 is decomposed. If necessary, each of the blocks must be decomposed.

Decomposition is a scientific method that uses the structure of a problem and allows you to replace the solution of one large problem with the solution of a series of smaller problems.

16. Morphological description and modeling of systems. Description of the structure of the system and the relationships between elements.

morphological description should give an idea of the structure of the system (morphology is the science of form, structure). Depth of description, level of detail, i.e. the definition of which components of the system will be considered as elementary (elements) is determined by the purpose of the description of the system. The morphological description is hierarchical. The morphology configuration is given at as many levels as are required to represent the basic properties of the system.

The goals of structural analysis are:

development of rules for the symbolic display of systems;

assessment of the quality of the system structure;

study of the structural properties of the system as a whole and its subsystems;

development of a conclusion on the optimality of the structure of the system and recommendations for its further improvement.

In the structural approach, two stages can be distinguished: determination of the composition of the system, i.e. a complete enumeration of its subsystems, elements, and clarification of the relationships between them.

The study of the system morphology begins with the elemental composition. He might be:

homogeneous (elements of the same type);

heterogeneous (various elements);

mixed.

Uniformity does not mean complete identity and determines only the proximity of the main properties.

Homogeneity, as a rule, is accompanied by redundancy and the presence of hidden (potential) opportunities, additional reserves.

Heterogeneous elements are specialized, they are economical and can be effective in a narrow range of environmental conditions, but quickly lose effectiveness outside this range.

Sometimes the elemental composition cannot be determined - indefinite.

An important feature of morphology is the purpose (properties) of elements. Distinguish elements:

informational;

energy;

real.

It should be remembered that such a division is conditional and reflects only the prevailing properties of the element. In the general case, the transfer of information is not possible without energy, the transfer of energy is not possible without information.

Information elements are intended for receiving, storing (storing), converting and transmitting information. The transformation may consist in changing the type of energy that carries information, in changing the method of encoding (representing in some sign form) information, in compressing information by reducing redundancy, decision making, etc.

There are reversible and irreversible transformations of information.

Reversible are not associated with the loss (or creation of new) information. Accumulation (memorization) is reversible if there is no loss of information during the storage time.

Energy transformation consists in changing the parameters of the energy flow. The input energy flow can come from outside, or from other elements of the system. The output energy flow is directed to other systems or to the environment. The process of energy conversion naturally needs information.

The process of transformation of a substance can be mechanical (for example, stamping), chemical, physical (for example, cutting), biological. In complex systems, the transformation of matter is of a mixed nature.

In the general case, it should be borne in mind that any processes, one way or another, lead to the transformation of matter, energy and information.

The morphological properties of the system essentially depend on the nature of the links between the elements. The concept of connection is included in any definition of a system. It simultaneously characterizes both the structure (statics) and the functioning (dynamics) of the system. Links ensure the emergence and preservation of the structure and properties of the system. Allocate informational, material and energy connections, defining them in the same sense in which the elements were defined.

The nature of the connection is determined by the specific weight of the corresponding component (or objective function).

Communication is characterized by:

direction,

force,

view.

According to the first two signs, connections are divided into directed and non-directed, strong and weak, and by nature - subordination, generation (genetic), equal and control connections.

Some of these links can be broken down in even more detail. For example, links of subordination on the links “genus-species”, “part-whole”; connections of generation - "cause-effect".

They can also be divided according to the place of application (internal - external), according to the direction of the processes (direct, reverse, neutral).

Direct connections are intended for the transfer of matter, energy, information or their combinations from one element to another in accordance with the sequence of functions performed.

The quality of communication is determined by its bandwidth and reliability.

A very important role, as we already know, is played by feedback - they are the main self-regulation and development of systems, their adaptation to changing conditions of existence. They mainly serve for process control and information feedback is the most common.

Neutral connections are not related to the functional activity of the system, they are unpredictable and random. However, neutral links can play a certain role in the adaptation of the system, serve as an initial resource for the formation of direct and reverse links, and be a reserve.

The morphological description may include indications of the presence and type of connection, contain a general description of the connection or their qualitative and quantitative assessments.

Structural properties of systems are determined by the nature and stability of relationships between elements. According to the nature of the relationship between the elements of the structure, they are divided into:

multi-connected,

hierarchical,

mixed.

The most stable are deterministic structures in which relations are either constant or change in time according to deterministic laws. Probabilistic structures change in time according to probabilistic laws. Chaotic structures are characterized by the absence of restrictions, the elements in them come into contact in accordance with individual properties. Classification is made according to the dominant feature.

The structure plays a major role in the formation of new properties of the system, different from the properties of its components, in maintaining the integrity and stability of its properties in relation to changes in the elements of the system within certain limits.

Important structural components are the relations of coordination and subordination.

Coordination expresses the ordering of the elements of the system "horizontally". Here we are talking about the interaction of components of the same level of organization.

Subordination - "vertical" ordering of subordination and subordination of components. Here we are talking about the interaction of components of different levels of the hierarchy.

Hierarchy (hiezosazche - sacred power, Greek) is the arrangement of the parts of the whole in order from the highest to the lowest. The term "hierarchy" (multi-stage) defines the ordering of system components in order of importance. Between the levels of the hierarchy of the structure, there can be relationships of strict subordination of the components of the lower level to one of the components of the higher level, i.e. tree-order relationships. Such hierarchies are called strong or tree-type hierarchies.

However, tree-like relationships do not have to exist between the levels of the hierarchical structure. Relationships can also occur within the same hierarchy level. An underlying component may be subordinate to several components of a higher level - these are hierarchical structures with weak links.

Hierarchical structures are characterized by the presence of managerial and executive components. There may be components that are both control and executive.

There are strictly and non-strictly hierarchical structures.

The system of a strict hierarchical structure has the following features:

the system has one main control component, which has at least two links;

there are executive components, each of which has only one connection with the higher-level component;

communication exists only between components belonging to two neighboring levels, while the components of the lower level are associated with only one component of the higher level, and each component of the higher level is associated with at least two components of the lower one. Fig.1

Rice. 2.

Figure 1 shows a graph of a strictly hierarchical structure, Figure 2 shows a graph of a non-strict hierarchical structure. Both structures have three levels.

So in Fig. 1, the element of the 1st level of the hierarchy can represent the rector of the university, the elements of the 2nd level - vice-rectors, the 3rd level - deans, the remaining elements (4th level, not shown in the figure) will represent the heads of departments. It is clear that all the elements and connections of the presented structure are not equal.

As a rule, the presence of a hierarchy is a sign of a high level of organization of the structure, although there may be non-hierarchical highly organized systems.

Functionally, hierarchical structures are more economical.

For non-hierarchical structures, there are no components that are only control or only executive. Any component interacts with more than one component.

Rice. 3 - Graph of the multiply connected structure of the system

Rice. 4 - Graph of the cellular structure of the system

Mixed structures are various combinations of hierarchical and non-hierarchical structures.

Let's introduce the concept of leadership.

A leading subsystem is one that satisfies the following requirements:

the subsystem does not have a deterministic interaction with any subsystem;

the subsystem is control (with direct or indirect interaction) in relation to the part (the largest number of subsystems);

a subsystem is either not controlled (subordinate) or controlled by the smallest (compared to others) number of subsystems.

There can be more than one leading subsystem, with several leading subsystems, the main leading subsystem is possible. The subsystem of the highest level of the hierarchical structure must simultaneously be the main leading one, but if this is not the case, then the proposed hierarchical structure is either unstable or does not correspond to the true structure of the system.

Mixed structures are various combinations of hierarchical and non-hierarchical structures. The stability of the structure is characterized by the time of its change. A struct can be changed without class conversion or by converting one class to another. In particular, the emergence of a leader in a non-hierarchical structure can lead to its transformation into a hierarchical one, and the emergence of a leader in a hierarchical structure can lead to the establishment of a limiting and then deterministic connection between the leading subsystem and the top-level subsystem. As a result, the top-level subsystem is replaced by the leading subsystem, or merged with it, or the hierarchical structure is transformed into a non-hierarchical (mixed) one.

Equilibrium structures are called non-hierarchical structures without leaders. Most often, multiply connected structures are equilibrium. Equilibrium does not mean the component-by-component identity of metabolism, it is only about the degree of influence on decision-making.

A feature of hierarchical structures is the absence of horizontal links between elements. In this sense, these structures are abstract constructions, since in reality it is difficult to find a production or any other operating system with missing horizontal connections.

In the morphological description of a system, its compositional properties are of great importance. The compositional properties of systems are determined by the way elements are combined into subsystems. We will distinguish subsystems:

effector (capable of transforming the impact and acting with matter or energy on other subsystems and systems, including the environment),

receptor (capable of converting external influences into information signals, transmitting and transferring information)

reflexive (capable of reproducing processes within themselves at the information level, generating information).

The composition of systems that do not contain (up to the elemental level) subsystems with pronounced properties is called weak. The composition of systems containing elements with pronounced functions is called, respectively, with effector, receptor or reflexive subsystems; combinations are possible. The composition of systems that include subsystems of all three types will be called complete. Elements of the system (i.e., subsystems into which morphological analysis does not extend) can have effector, receptor, or reflex properties, as well as their combinations.

In set-theoretic language, a morphological description is a quadruple:

SM = (S, V, d, K),

where S=(Si)i is the set of elements and their properties (in this case, an element is understood as a subsystem, into which the morphological description does not penetrate); V =(Vj)j - set of connections; δ - structure; K - composition.

We consider all sets to be finite.

We will distinguish in S:

Composition:

homogeneous,

heterogeneous,

mixed (a large number of homogeneous elements with a certain number of heterogeneous),

uncertain.

Element properties:

information,

energy,

information and energy,

material and energy,

indefinite (neutral).

We will distinguish in the set V:

Purpose of links:

information,

real,

energy.

The nature of the connections:

straight,

reverse,

neutral.

We will distinguish in d:

Structural stability:

deterministic

probabilistic

chaotic.

Buildings:

hierarchical,

multi-connected,

mixed,

transforming.

We will distinguish in the set K:

Compositions:

weak,

with effector subsystems,

with receptor subsystems,

with reflective subsystems,

full,

indefinite.

The morphological description, as well as the functional one, is built according to the hierarchical (multi-level) principle by sequential decomposition of subsystems. The levels of decomposition of the system, the levels of the hierarchy of the functional and morphological description must match. The morphological description can be performed by sequential dissection of the system. This is convenient if the connections between subsystems of the same hierarchy level are not too complex. The most productive (for practical problems) are descriptions with a single articulation or with a small number of them. Each element of the structure can, in turn, be described functionally and informationally. The morphological properties of the structure are characterized by the time it takes to establish a connection between the elements and the throughput of the connection. It can be proved that the set of structure elements forms a normal metric space. Therefore, it is possible to define a metric (the concept of distance) in it. To solve some problems, it is expedient to introduce a metric in the structural space.

17. Methods for describing structures in morphological description. Structure graphs.

Block diagrams- The formation of the structure is part of the solution of the general problem of describing the system. The structure reveals the general configuration of the system, and does not define the system as a whole.

If we depict the system as a set of blocks that carry out some functional transformations, and the connections between them, then we get a block diagram that describes the structure of the system in a generalized form. A block is usually understood, especially in technical systems, as a functionally complete and designed as a separate whole device. Division into blocks can be carried out on the basis of the required degree of detail in the description of the structure, the visibility of the display in it of the features of the functioning processes inherent in the system. In addition to functional ones, logical blocks can be included in the block diagram, allowing you to change the nature of the operation depending on whether some predetermined conditions are met or not.

Structural diagrams are visual and contain information about a large number of structural properties of the system. They are easy to refine and concretize, during which it is not necessary to change the entire scheme, but it is enough to replace its individual elements with block diagrams that include not one, as before, but several interacting blocks.

However, a block diagram is not yet a structure model. It is difficult to formalize and is rather a natural bridge facilitating the transition from a meaningful description of the system to a mathematical description than a real tool for analyzing and synthesizing structures. Rice. - Block diagram example

Counts - The relations between the elements of the structure can be represented by a corresponding graph, which makes it possible to formalize the process of studying time-invariant properties of systems and to use the well-developed mathematical apparatus of graph theory.

Definition. A graph is a triple G=(M, R, P), where M is a set of vertices, R is a set of edges (or graph arcs), P is the incidence predicate of graph vertices and edges. P(x, y, r) = 1 means that the vertices x, y∈ M are incident (connected, lie on) an edge of the graph r∈ R.
To make it easier to work with a graph, its vertices are usually numbered. A graph with numbered vertices is called marked.

Each edge of the graph connects two vertices, which in this case are called adjacent. If the graph is marked, then the edge is given by the pair (i,j), where i and j are the numbers of adjacent vertices. Obviously, the edge (i,j) is incident to the vertices i and j , and vice versa.

If all the edges of the graph are given by ordered pairs (i, j), in which the order of the adjacent vertices matters, then the graph is called directed. An undirected graph contains no directed edges. In a partially directed graph, not all edges are directed.

Geometrically, graphs are depicted as diagrams, on which vertices are displayed as points (circles, rectangles), and edges as segments connecting adjacent vertices. An oriented edge is defined by a segment with an arrow.

The use of diagrams is so widespread that when people talk about a graph, they usually think of a diagram of a graph.

If the edges of a graph have some numerical connection characteristics, then such graphs are called weighted. In this case, the incidence matrix contains the weights of the corresponding links, the sign before the number determines the direction of the edge.

An important characteristic of a structural graph is the number of possible paths that can be taken from one vertex to another. The more such paths, the more perfect the structure, but the more redundant it is. Redundancy ensures the reliability of the structure. For example, the destruction of 90% of the neural connections of the brain is not felt and does not affect behavior. There can also be useless redundancy, which is represented as loops in the structural graph.

18. Structure of system analysis. Basic decision cycle. Function tree.

The general approach to problem solving can be represented as a cycle.

At the same time, in the process of functioning of a real system, the problem of practice is revealed as a discrepancy between the existing state of affairs and the required one. To solve the problem, a systematic study (decomposition, analysis and synthesis) of the system is carried out, which removes the problem. During the synthesis, the analyzed and synthesized systems are evaluated. The implementation of the synthesized system in the form of the proposed physical system allows us to assess the degree of removal of the problem of practice and make a decision on the functioning of the modernized (new) real system.

With this view, another aspect of the definition of a system becomes apparent: the system is a means of solving problems.

The main tasks of system analysis can be represented as a three-level tree of functions.

At the stage of decomposition, which provides a general representation of the system, the following are carried out:

Definition and decomposition of the general goal of the study and the main function of the system as a restriction of the trajectory in the state space of the system or in the area of admissible situations. Most often, decomposition is carried out by constructing a tree of goals and a tree of functions.

Isolation of the system from the environment (separation into a system / "non-system") according to the criterion of participation of each considered element in the process, leading to a result based on the consideration of the system as an integral part of the supersystem.

Description of influencing factors.

Description of development trends, uncertainties of various kinds.

Description of the system as a "black box".

Functional (by functions), component (by type of elements) and structural (by type of relations between elements) decomposition of the system.

Depth of decomposition is limited. The decomposition must stop if it is necessary to change the level of abstraction - to present the element as a subsystem. If during decomposition it turns out that the model begins to describe the internal algorithm of the element’s functioning instead of the law of its functioning in the form of a “black box”, then in this case the level of abstraction has changed. This means going beyond the goal of studying the system and, therefore, causes the decomposition to stop.

In automated methods, the decomposition of the model to a depth of 5-6 levels is typical. One of the subsystems is usually decomposed to such a depth. Functions that require this level of detail are often very important, and their detailed description provides the key to the secrets of how the entire system works.

It has been proven in general systems theory that most systems can be decomposed into basic representations of subsystems. These include: serial (cascade) connection of elements, parallel connection of elements, connection using feedback.
The problem of decomposition is that in complex systems there is no one-to-one correspondence between the law of functioning of subsystems and the algorithm, its implementation. Therefore, the formation of several options (or one option, if the system is displayed as a hierarchical structure) of the system decomposition is carried out.

Let's look at some of the most commonly used decomposition strategies.

Functional decomposition. Decomposition is based on the analysis of system functions. This raises the question of what the system does, regardless of how it works. The division into functional subsystems is based on the commonality of functions performed by groups of elements.

Decomposition by life cycle. A sign of the allocation of subsystems is a change in the law of functioning of subsystems at different stages of the cycle of existence of the system "from birth to death". It is recommended to apply this strategy when the goal of the system is to optimize processes and when it is possible to determine the successive stages of converting inputs to outputs.

Decomposition by physical process. A sign of subsystem selection is the steps of the subsystem functioning algorithm execution, the stages of changing states. While this strategy is useful in describing existing processes, it can often result in a system description that is too coherent and does not take full account of the limitations that functions impose on one another. In this case, the control sequence may be hidden. This strategy should be applied only if the purpose of the model is to describe the physical process as such.

Decomposition by subsystems (structural decomposition). A sign of subsystem allocation is a strong connection between elements according to one of the types of relations (connections) existing in the system (informational, logical, hierarchical, energy, etc.). The strength of communication, for example, according to information, can be estimated by the coefficient of information interconnection of subsystems k = N / N0, where N is the number of mutually used information arrays in subsystems, N0 is the total number of information arrays. To describe the entire system, a composite model must be built that combines all the individual models. It is recommended to use decomposition into subsystems only when such division into the main parts of the system does not change. The instability of the boundaries of subsystems will quickly devalue both individual models and their combination.

At the analysis stage, which provides the formation of a detailed representation of the system, the following are carried out:

Functional and structural analysis of the existing system, which allows to formulate requirements for the system being created. It includes specification of the composition and laws of functioning of elements, algorithms of functioning and mutual influences of subsystems, separation of controlled and uncontrolled characteristics, setting the state space Z, setting the parametric space T, in which the behavior of the system is set, analyzing the integrity of the system, formulating requirements for the system being created.

Morphological analysis - analysis of the relationship of components.

Genetic analysis - analysis of the background, the reasons for the development of the situation, existing trends, making forecasts.

Analysis of analogues.

Analysis of efficiency (in terms of effectiveness, resource intensity, efficiency). It includes the choice of a measurement scale, the formation of performance indicators, the justification and formation of performance criteria, the direct evaluation and analysis of the obtained assessments.

Formation of requirements for the system being created, including the choice of evaluation criteria and restrictions.

The stage of synthesis of the system that solves the problem is presented in the form of a simplified functional diagram in the figure. At this stage, the following are carried out:

Development of a model of the required system (selection of a mathematical apparatus, modeling, evaluation of the model according to the criteria of adequacy, simplicity, correspondence between accuracy and complexity, balance of errors, multivariate implementations, block construction).

Synthesis of alternative structures of the system that removes the problem.

Synthesis of the parameters of the system that removes the problem.

Evaluation of variants of the synthesized system (substantiation of the evaluation scheme, implementation of the model, evaluation experiment, processing of evaluation results, analysis of results, selection of the best variant).

Rice. - Simplified functional diagram of the stage of synthesis of the system solving the problem

An assessment of the degree of removal of the problem is carried out at the completion of the system analysis.

The most difficult to perform are the stages of decomposition and analysis. This is due to the high degree of uncertainty that needs to be overcome in the course of the study.

19. 9 stages of system representation formation.

Stage 1. Identification of the main functions (properties, goals, purpose) of the system. Formation (selection) of the main subject concepts used in the system. At this stage, it is about understanding the main outputs in the system. This is the best place to start your research. The type of output must be determined: material, energy, information, they must be attributed to some physical or other concepts (production output - products (what?), Control system output - command information (for what? in what form?), output of an automated information system - information (about what?), etc.).

Stage 2. Identification of the main functions and parts (modules) in the system. Understanding the unity of these parts within the system. At this stage, the first acquaintance with the internal content of the system takes place, it is revealed what large parts it consists of and what role each part plays in the system. This is the stage of obtaining primary information about the structure and nature of the main links. Such information should be presented and studied using structural or object-oriented methods of system analysis, where, for example, the presence of a predominantly serial or parallel nature of the connection of parts, mutual or predominantly unilateral direction of influences between parts, etc. Already at this stage, attention should be paid to the so-called system-forming factors, i.e. on those connections, interdependencies that make the system a system.

Stage 3. Identification of the main processes in the system, their role, conditions for implementation; identification of staging, jumps, changes of states in functioning; in systems with control - the allocation of the main control factors. Here, the dynamics of the most important changes in the system, the course of events are studied, state parameters are introduced, the factors influencing these parameters that ensure the course of processes, as well as the conditions for the beginning and end of processes, are considered. It is determined whether the processes are manageable and whether they contribute to the implementation of the system's main functions. For controlled systems, the main control actions, their type, source and degree of influence on the system are clarified.

Stage 4. Identification of the main elements of the "non-system" with which the system under study is associated. Identification of the nature of these relationships. At this stage, a number of individual problems are solved. The main external influences on the system (inputs) are investigated. Their type (material, energy, information), the degree of influence on the system, and the main characteristics are determined. The boundaries of what is considered a system are fixed, the elements of the “non-system” are determined, to which the main output effects are directed. Here it is also useful to trace the evolution of the system, the path of its formation. Often this is what leads to an understanding of the structure and features of the functioning of the system. In general, this stage allows you to better understand the main functions of the system, its dependence and vulnerability or relative independence in the external environment.

Stage 5. Identification of uncertainties and accidents in the situation of their determining influence on the system (for stochastic systems).

Stage 6. Identification of a branched structure, hierarchy, formation of ideas about the system as a set of modules connected by inputs and outputs.

Stage 6 ends with the formation of general ideas about the system. As a rule, this is enough if we are talking about an object with which we will not work directly. If we are talking about a system that needs to be studied for its in-depth study, improvement, management, then we will have to go further along the spiral path of in-depth study of the system.

Formation of a detailed representation of the system

Stage 7. Identification of all elements and relationships important for the purposes of the review. Their assignment to the hierarchy structure in the system. Ranking of elements and links according to their importance.

Stages 6 and 7 are closely related to each other, so it is useful to discuss them together. Stage 6 is the limit of cognition "inside" a rather complex system for a person who operates it entirely. More in-depth knowledge of the system (stage 7) will have only a specialist responsible for its individual parts. For a not too complex object, the level of stage 7 - knowledge of the whole system - is achievable for one person. Thus, although the essence of stages 6 and 7 is the same, but in the first of them we are limited to the reasonable amount of information that is available to one researcher.

With in-depth detailing, it is important to single out exactly the elements (modules) and connections that are essential for consideration, discarding everything that is not of interest for the purposes of the study. Cognition of the system does not always mean only separating the essential from the non-essential, but also focusing attention on the more essential. Detailing should also affect the connection of the system with the “non-system”, already considered in stage 4. At stage 7, the set of external relations is considered clarified to such an extent that one can speak of a thorough knowledge of the system.

Stages 6 and 7 summarize the overall, integral study of the system. Further stages already consider only its individual aspects. Therefore, it is important to once again pay attention to the system-forming factors, to the role of each element and each connection, to understanding why they are exactly like that or should be exactly like that in terms of the unity of the system.

Stage 8. Accounting for changes and uncertainties in the system. Here we study a slow, usually undesirable change in the properties of the system, which is commonly called "aging", as well as the possibility of replacing individual parts (modules) with new ones, which allow not only to resist aging, but also to improve the quality of the system compared to the original state. Such improvement of an artificial system is usually called development. It also includes improving the characteristics of modules, connecting new modules, accumulating information for its better use, and sometimes restructuring the hierarchy of connections.

The main uncertainties in a stochastic system are considered to be investigated at stage 5. However, indeterminacy is always present in a system that is not designed to work in conditions of a random nature of inputs and connections. Let us add that the consideration of uncertainties in this case usually turns into a study of the sensitivity of the most important properties (outputs) of the system. Sensitivity is understood as the degree of influence of a change in inputs on a change in outputs.

Stage 9. Study of functions and processes in the system in order to manage them. Introduction of management and decision-making procedures. Control actions as control systems. For purposeful and other systems with control, this stage is of great importance. The main control factors were understood in stage 3, but there it was in the nature of general information about the system. In order to effectively introduce controls or study their effects on system functions and processes, deep knowledge of the system is required. That is why we are talking about the analysis of controls only now, after a comprehensive consideration of the system. Recall that management can be extremely diverse in content - from commands of a specialized control computer to ministerial orders.

However, the possibility of a uniform consideration of all targeted interventions in the behavior of the system makes it possible to speak not about individual management acts, but about a management system that is closely intertwined with the main system, but clearly stands out in terms of functionality.

At this stage, it is clarified where, when and how (at what points in the system, at what moments, in what processes, jumps, selections from the population, logical transitions, etc.) the control system affects the main system, how effective it is, acceptable and conveniently implemented. When introducing controls in the system, options for translating inputs and constant parameters into controlled ones should be investigated, acceptable control limits and methods for their implementation should be determined.

After the completion of stages 6-9, the study of systems continues at a qualitatively new level - a specific stage of modeling follows. We can talk about creating a model only after a complete study of the system.

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System methods and procedures. What types of mathematical models according to the construction method do you ...

BASICS OF THE SYSTEM CONCEPT: CONCEPTS, ESSENCE, ATTRIBUTES

Program annotation

The origin of the concept of system. System integrity. The evolution of views on the system. Approaches to the definition of the system. Properties of the socio-economic system.

System description language. Concepts characterizing the structure and activity of the system. System element. Wednesday. Connection. System integrity. Purpose of the system.

system attributes. Integrity is the root attribute of the system. Emergence and its manifestation in the system.

External environment and system. Closed (closed) and open systems.

Concepts characterizing the structure and functioning of the system. System structure. Network and hierarchical structures. The complexity of the system and approaches to its definition The state and parameters of the system. Static and dynamic systems. System behavior. Situation. Perturbations.

Reference abstract of the lecture

2.1. Definition of the concept of a system. The amazing unity and harmony of the universe has long struck the imagination of people. The incomprehensible complexity and interdependence of phenomena and processes did not give rest to either ancient thinkers or their current descendants - physicists, biologists, cybernetics, philosophers, economists . In an effort to uncover the source of the self-movement of nature and society, to recognize in them cause-and-effect relationships and patterns, researchers from generation to generation enriched knowledge about systems and moved towards a modern understanding of them.

The category “system” owes its origin to the Greek wordsystema, meaning in translation “a whole, made up of parts, a connection". In those ancient times, when the sages of Ancient Greece created their doctrine of the structure of the Universe and painfully searched for its driving principle, the view of systems began to take shape. From the penetrating gaze of Heraclitus, Democritus, Aristotle did not escape the complexity and inconsistency of the systems they contemplate, be it star clusters or cultivated cereals.

Notable in this respect is the view of Heraclitus. He believed that the world has always been, is and will be an ever-living fire, naturally ignited and again naturally extinguished. Everything flows, but in this flow the logos (world mind) as a law dominates. At the same time, opposites are united in everything and there is a hidden harmony.

Meanwhile, the above definition of the system, noting its most important quality - integrity, was too general and abstracted from the features inherent in the system. It became obvious that integrity is given to the system by the articulation of its elements, due to which it differs from a simple sum, the totality of its components. Therefore, it turned out to be necessary to comprehend the concepts of the whole and the part and the relationship between them.

Interest in the problem of the whole and the part was already shown in deep antiquity. Thus, Aristotle understood the essence of these categories as follows: “A whole is that which does not lack any of those parts, consisting of which it is called a whole by nature, and also that which embraces the things it embraces so that the latter form something one …”. Thus, the whole not only combines its parts, but also acts as a qualitatively new formation.

The elucidation of the nature of the whole and its parts led to the study of the mode of their interactions, which are established between the elements and give rise to the system as such. As a result, the definition of the system began to include existing in it connections between elements.

As a result, systems began to be called “a set of elements that are in relationships and connections with each other, forming a certain integrity, unity. Quoted from the Big Encyclopedic Dictionary, This definition of the system is the most universal and common today. Its advantage is the irrelevance to the nature of systems, which imposes specificity on their structure and functioning and can be taken into account in defining a specific system..

In a number of definitions, attention is reasonably focused on the multi-connectedness and interdependence of the elements of the system, which is why it cannot be decomposed into autonomous parts. In the latter case, the system passes into a different quality or simply loses itself.

By the way, Hegel noticed this outcome: “The whole, although it consists of parts, ceases, however, to be a whole when it is divided ...”. Hence, the integrity of the system implies the absence of any isolated parts in it, i.e., not covered by interactions with other parts of the system.

On this basis, the dependence property extends to all elements of the system without exception, which is why its interpretation implies the interaction of all elements and the inseparability of the system.

An example of such a definition is the interpretation of the system by R. Ackoff and F. Emery, by which they mean “a set of interconnected elements, each of which is connected directly or indirectly with each other element, and any two subsets of this set cannot be independent.”

At the same time, some analysts see incompleteness in such an interpretation of the system, considering it necessary to point out its researcher (observer). The fact is that the boundaries and content of the system are largely determined by the approach and capabilities of the person (team) who studies or constructs it. Therefore, the same system, studied from a different angle of view, can be studied and described in different ways.

An English neurophysiologist draws attention to this circumstance, in particular. In his opinion, if the system becomes larger and larger in the course of research, information about it increases dramatically and its perception becomes impossible. Then the goal “should be to obtain partial knowledge, which, being partial in relation to the whole, would nevertheless be complete in itself and sufficient for solving a given practical problem.”

Finally, systems that have behavior are significantly different from others - the so-called behavioral (from the English. вehaviour - behavior) systems. Since the subject of our consideration are socio-economic systems, it is necessary to supplement its definition purpose creating a system. The target setting plays a decisive role for such systems, setting for it the internal structure and nature of functioning.

Thus, generalizing the properties of the socio-economic system, we can formulate the following definition of it.

The socio-economic system is a set of interconnected elements characterized within the framework of the research task by integrity and purposeful behavior.

The present interpretation of the system follows from its main features and provides only preliminary information about the system. In the future, as knowledge about it deepens, the given definition of the system will be expanded and specified.

Organizing the existing approaches to the definition of the system in the literature, analysts tend to divide them into 3 groups.

The first group covers objectively existing complexes of processes and phenomena interconnected (say, travel companies, hotels, health care institutions, banks, etc.).

The second group includes artificially developed systems, for example, models of the functioning of certain enterprises. These systems serve as a reflection of real phenomena and processes and serve as a tool for their study.

The third group includes combined systems that have features of the first and second groups. These are the designed and created enterprises and their divisions, in the implementation of which methods and modeling tools are used.

Of course, it is hardly possible to give an exhaustive definition of the system. And not only because the systems are diverse, have an infinite number of properties, and it is rather difficult to bring them under a “common denominator”. After all over time, our knowledge about the system grows, as a result of which the very definition of the system is rethought and refined. Just as systems live and develop, so does the concept of it.

2.2. Concepts that characterize the content of the system. The study and design of systems involves the use of a certain language for its description. It should be sufficiently informative, capacious in content to cover the problems of systems and at the same time not allow ambiguity. Otherwise, difficulties may arise both with the completeness of the presentation of the material and with understanding its essence.

Consequently it is appropriate to dwell on the basic concepts that characterize the structure and activity of socio-economic systems. Let us reveal the content of those of them that constitute the terminological minimum of systems theory and will be required for us in what follows. First of all, let us turn to the categories that reveal the concept of a system.

System element - this is its smallest link in the framework of the study. In other words, its primary cells, which in a particular analysis of the system are not subject to fragmentation and form an idea of its structure and behavior. Depending on the purpose and specifics of the task, various parts of the system can be taken as an element: a workplace, an office, a department, a site, a workshop, a branch, an enterprise, an association, etc.

Wednesday is a set of elements taken into account, their properties and characteristics. In this set, it is customary to single out a certain set of elements that form the system under study, and the remaining elements surrounding it. They say that the former constitute the internal, the latter - the external environment of the system. Such a division of the environment into internal and external is conditional, and the boundary between them is determined by the criterion for distinguishing the system. This criterion is usually set by the external environment, dictated by the considerations of the study, and therefore often during its rethought and refined.

The properties of the environment find expression in the diversity, interdependence, variability and certainty of the values of its factors.

Obviously, the greater the diversity and variability of environmental factors, the more difficult it is to analyze. At the same time, the rate of change in the values of factors characterizes the degree of mobility of the environment, its dynamism. And the certainty of the values of factors, that is, the completeness and accuracy of information about them, gives the environment one or another“transparency” and influences the process of its reproduction by formal means.

Connection is a constraint imposed on the elements of the system. Forming a connection, the elements lose part of their freedom, but at the same time they acquire the ability to come into contact with each other.

Connections exist both within a certain system and with the external environment. Through external connections, the system “communicates” with its environment, with the help of internal connections, the elements of the system interact with each other and maintain its integrity. Distinguish between rigid, time-invariant connections, and flexible, which can change in time. system operation. It must be borne in mind that from the standpoint of management, communication is the exchange of information between the elements of the system, which ensures its purposeful behavior. At the same time, one can also meet direct and indirect, strong and weak, directed and non-directed, direct and feedback.

System Integrity - this is its organic unity, expressed by the isolation of the elements of a given system from other elements of the external environment and the ability of the system to self-preserve. Its integrity is ensured primarily by the fact that the internal connections of the system are stronger than external ones, and therefore it is possible to resist the negative effects of the environment and avoid the collapse of the system. On the other hand, its integrity is supported by the emergence of new integrative properties in the system, which induces its elements to come into contact with each other and follow collective behavior.

In the methodological aspect, the following should be noted here. Since integrity takes precedence over other properties of the system, it is the system as a whole that dominates in interaction with the elements, and not vice versa. Elements make up a system, but at the same time, it subordinates its elements to itself and, when splitting, generates them. After all, the division of the system into elements can be done in various ways, but its integrity does not change from this.

Purpose of the system is her intention regarding the result of her activities over a period of time. “The desire to co-produce the achievement of common goals is what produces interactions that unite individuals into a social group” (). Thus, the goal acts as a driving motive for the formation of the system, a prerequisite for its functioning and integrity.

The discussed concepts are initial for the definition of the system. In the future, this terminology will be refined and expanded as the attributes and patterns of system behavior are studied.

2.3. system attributes.The root attribute of the system - its integrity - is ensured by the emergence of new qualities in the system, which are absent from its elements separately. It is these integrative properties that make the system unique and determine the specifics of its activity.

In foreign systemology, this phenomenon is called emergence(from Latinemergere), which in translation means “appear, arise”. At the same time, the fundamental irreducibility of the properties of the system to the sum of the properties of its constituent elements and non-derivability from the last properties of the system. This emphasizes the qualitative novelty of the emergent properties of the system: they cannot be obtained by simply adding the properties of its elements, although the properties of the elements, of course, leave an imprint on the properties of the system.

The effects of the system and its elements are distinguished by their mutual influence on each other: the system affects the elements, the elements affect the system. As a result, the elements lose some properties that they had in a free (before entering the system) position, but instead acquire other properties arising from their place and functions in the system. Similarly, the system undergoes changes if new elements are included in it or old elements are excluded. By the way, in the process of interaction of the elements of the system, it can acquire not only new properties, but also parts that were absent from the system before. Thus, the system approach has structural and functional aspects.

External environment and system. It has already been noted above that the division of the environment into external and internal is to a certain extent conditional and is introduced by the researcher. Such a delimitation of some elements from others makes it possible to outline the system in the environment, but at the same time emphasizes the inseparability of the system from its external environment. That's why the functioning of the system takes place in the external environment and requires consideration of their interaction.

Closed (closed) system is a system that does not have channels of exchange with the external environment. In other words, not a single element of the system is connected with any element of the external environment. When considering such an idealized system, the influence of the external environment is neglected, believing that the system is autonomous and remains “impenetrable” to its influence. Therefore, a change in the states of a closed system can be caused only by some of its internal causes.

open system – it is a system that has channels of exchange with the external environment and is influenced by it. In such systems, at least one of its elements is associated with an element of the external environment. In the general case, interaction with the environment can be of a diverse nature: material and energy, personnel, financial, informational, and others. Thus, open systems are susceptible to environmental influences, able to respond to them and change their mode of operation.

In reality, systems cannot isolate themselves from their environment and are therefore open. Meanwhile, sometimes analysts neglect the influences of the medium (for example, gravitational, magnetic, etc.) that are insignificant within the framework of a particular task and represent such a system as closed, while allowing a certain error.

2.4. Concepts characterizing the structure and functioning of the system. Achieving the goal involves subordinating to it the internal structure of the system and the activities of all its members. elements. In conditions of increasing complexity of the external and internal environment, the purposeful movement of the system finds expression in the multiplicity and scale of the functions performed by the elements. As a result, there is a need for a rational implementation of the interaction of the elements of the system, for which its structure is formed.

System Structure is a set of its basic elements, connections and relations between them, as well as ways of interaction of elements. It represents the “skeleton” of the system, its invariant, i.e., such a quality of the system that remains relatively stable when the mode of its operation changes. The structure as a network of essential connections between elements performs a system-forming and system-preserving role in the system, thereby ensuring its integrity.

Meanwhile, the relative constancy of the structure does not mean at all that it remains unchanged during the functioning of the system. On the contrary, the mobility of the system would be impossible if its structure was ossified and not subjected to change. But at the same time, there is a limit to the dynamism of the structure, beyond which comes the transition of the system to a new quality or its collapse.

The above definition of the structure of a system is close in its content to the concept of a system, which can confuse their interpretation. How do they differ from each other? The structure is formed only by stable elements and connections, while the system is formed by the totality (both stable and unstable) of elements and connections present in it. That is why structural bonds protect the system from destruction, despite the interference that occurs inside and outside the system.

The system operates in time and space. Therefore, depending on the dimension in which the interactions in the system are considered, it can be represented as a network or hierarchical structure.

A network structure (or simply a network) serves as a means of decomposing a system in time. Such a structure reflects the deployment of the process of the system functioning as events follow one after another and the connection between them. The task of research in this case is reduced to the analysis of chains of events and calculations of the duration of the critical path (the longest chain of events) and the reserves of events.

Hierarchical structure (hierarchy) is a means of system decomposition in space. It captures the interaction of elements distributed over levels in accordance with their inherent subordination. Such a vertical structure of the system is remarkable in that it allows you to combine directiveness with the provision of a certain freedom of maneuvering to lower elements. Hence, the main problem is to find a rational correlation of centralization-decentralization of the elements of the system in order to fully realize its capabilities to achieve the goal.

Obviously, the more elements in the system and the more numerous connections in it, the more branched its structure and the more complex the system. Therefore, it is necessary to clarify what we mean here by the category of complexity.

System complexity - it is the diversity of its elements and the connections between them. On this basis, we will judge the complexity of the system not only by whether there are many or few elements and connections in it, but also by their heterogeneity. This means that it is required to take into account the degree of similarity and difference of elements and connections, their ability to transform - change, die off and generate, etc. Hence the maximum complexity falls on living organisms and social systems. It is clear that the more complex the system, the less predictable its behavior and the more difficult it is to study.

There are various approaches to the classification of systems according to the level of complexity, among which the most famous are the following.

One of them takes the number of elements of the system as a classification feature. For example, a Soviet mathematician divides all systems into small (10-1000 elements), complex (00 elements) and so on - ultra-complex and super-systems. As an example of the system of the 2nd group, he cites the transport system of a large city, the 3rd group - animal and human organisms, social organizations, and the 4th group - the stellar universe.

Another approach to classification comes from the possibility of describing the system. So, the English cyberneticist S. Beer proposes to divide all systems into simple, complex and very complex. If the description of the first systems does not meet with difficulties, the second ones still lend themselves to a detailed description, then the third ones (the economy, the brain, the firm) are no longer there. At the same time, the author of the classification introduces the second criterion - the nature of the processes occurring in them (deterministic or probabilistic).

From the definition of the complexity of systems and their classification, it can be seen that the variety of elements and connections generates a set of possible states of the system, which form the process of its functioning.

State of the system – is its position at some point in time. The description of this situation is given by the values of the characteristics of the system fixed at the moment. Among them, there may be observable external influences on the system and its response.

The number of states of real systems is extremely large. For example, let's say that an element is described by 3 characteristics, each of which can take only 2 values. Then the number of states of such an element is 2 × 2 × 2 = 8. If the system is formed from 10 such elements, then the total number of states of the system will be 8 to the power of 10, i.e. more than 1 billion.

System Settings – these are its characteristics chosen for the purpose of studying this system. Parameters report those properties of the system that transfer it from one state to another. The procedure for selecting parameters is devoid of strict regulation and formalization, which is why it depends on the approach and experience of the researcher. However, the subjectivity of the procedure can be reduced due to the subsequent analysis and screening out of insignificant and uninformative parameters.

Depending on the ability to be in different states, systems can be static or dynamic.

Static system – it is a system that does not change over time. Since this system does not change states, it is assumed that it is in only one state. Such a system, despite the influence of the external environment, does not respond to its impact and is of little interest for research.

dynamic system – It is a system that can change its states over time. As a result, the processes occurring in it are distinguished by a variety of internal states and therefore richer properties. Further the subject of our study will be only open dynamical systems.

System Behavior – it is a sequence of its states in a certain space and time. In view of this, only those systems that can move from one state to another have behavior.. Note that some experts tend to believe that behavior is inherent only in organizational and human-machine systems, i.e., endowed with goal-setting, while in relation to other systems it is more appropriate to speak only about the processes occurring in them. In this case, it can be argued that behavior systems are formed under the influence of interdependent actions of the elements of the system aimed at achieving the desired result.

Situation – it is a set of states of the system and the environment at a fixed point in time. The situation characterizes the current state of the system and its environment through the values of their parameters.

In various situations, attention is drawn to such actions of the external and internal environment that interfere with the functioning of the system.

Disturbance (interference) – it is an action that affects the state of the system and destabilizes its behavior. It introduces discord in the interaction of elements and reduces the useful result of the functioning of the system. Perturbations can come from both the internal environment and the external. In other words, they can arise in the system itself under the influence of its own processes and in its environment.

Perturbations leave an imprint on the functioning of the system and cause it to change the values of its parameters, and sometimes the structure of the system. Therefore, the control of the system is designed to ensure its movement along the calculated trajectory specified by the system parameters.

THEME 2

SYSTEM FUNCTIONING PROCESS

Program annotation

Functional properties of the system. System balance. Static and dynamic balance. System stability. Region of stability. Stable balance.

Homeostasis. Adaptation. Development. Evolutionary and revolutionary development.

Organization and organization of the system. Order relations between its elements, connections and interactions.

Classification of systems according to the degree of organization. Well and badly organized systems. self-organizing systems.

Reference abstract of the lecture

3.1. Functional properties and characteristics of the system. The impact of the environment on an open system leads to a change in the conditions of its functioning and meets the response of the system.

System equilibrium – it is its ability to maintain its behavior in the absence of environmental disturbances. This situation in social systems is remarkable in that none of the interacting elements seeks to break it. Therefore, the state of equilibrium is often associated with the achievement of the desired position by the system.

Meanwhile, even in a state favorable for the system, in the course of its functioning it does not lose mobility and shifts relative to the equilibrium point in one direction or another. By oscillating around it, the system is in a state of not static, but dynamic equilibrium.

Sustainability – is the ability of a system to maintain its behavior despite environmental disturbances. Strictly speaking, the concept of stability refers not to the system as such, but to its parameters. The fact is that some parameters of the system may have the property of stability, while others may not. In this case, it is difficult to assess the stability of the system as a whole..

In addition, from a practical point of view, the questions of the conservation of which properties of the system are in question and what is the class of admissible perturbations are essential. After answering these questions, the efforts of researchers can be directed to determining the values of the parameters at which the system remains stable (the “stability region”). After all, with respect to other properties or restrictions on perturbations, the parameters of the system may turn out to be unstable.

sustainable balance – is the ability of a system to return to a state of equilibrium after it has been taken out of it. Since the system does not always assume the previous state of equilibrium, states of unstable equilibrium may also occur among them. In the general case, a system can have not one, but many different equilibrium states.

The property of stable equilibrium manifests itself in another property inherent in living organisms - homeostasis. In biology, homeostasis is understood as the ability of an organism to keep its parameters within physiologically acceptable limits. Meanwhile, technical systems equipped with self-regulation mechanisms can also have homeostatic behavior.

Adaptation – is the ability of the system to adapt to disturbances. As a result, the system has the ability to weaken the negative impact of external and internal disturbances and maintain itself as an integralsystem. Depending on the nature of disturbances, the process of system adaptation may include a change in the mode of its operation, or a radical restructuring of the system.

System development is a process of quantitative and qualitative changes in it that do not violate the integrity of the system. In the course of the development of the system, there is a change in complexity and a modification of the structure, i.e., transformations in the composition of the elements and the totality of connections between them. At the same time, two forms of development are distinguished - gradual (evolutionary) and abrupt (revolutionary) changes in the properties of the system. In addition, the direction of these changes can be different - ascending (progressive) or descending (regressive). In the latter case, the system loses its former qualities and degrades up to disintegration.

With progressive development, the structure of the system becomes more complex, for example, the company expands its technological base, which allows it to diversify production and adapt to fluctuations in demand for its goods and services. In contrast, regressive development proceeds with the aging of equipment, the depletion of working capital and the curtailment of the production and financial activities of the company.

3.2. Organization and organization of the system.Structural transformations in a system may result in an increase in the interconnectedness of its elements and the coherence of the functioning of parts of the system, or, conversely, in breaking the links between its elements and thereby increasing discord in the system. Therefore, the concept of system development can be considered from the point of view of its organization.

System organization - this is its structure, characterized by relations of order among the elements, connections and interactions between them. In this interpretation, the concept of system organization contains its structure and is defined through it. At the same time, relations of order between its elements, connections and interactions are additionally introduced into the interpretation of the organization of the system.

Under the relation of order between elements we mean the rule of their location in the space-time dimension. Here, the position of the elements relative to each other, their precedence, etc. are taken into account. In other words, if there is some regular occurrence of elements in the system, then we will consider it as an order relation between them.

Similarly, the relation of order between connections and interactions among elements, i.e., their regular implementation in the system, is also taken into account.

The observed relations in the system may differ from each other and be quite diverse. Because of this, the coordinated functioning of the elements of the system dictates the need to reduce this diversity and increase the coherence of their interaction, since otherwise chaos will grow in the system.

Organization of the system – this is the degree of orderliness of its functioning, achieved through the interaction of the elements of the system. Hence, the more and more closely connected the elements of the system are with each other, the better its organization. For a socio-economic system, this condition is expressed in the need to coordinate the behavior of all its elements, which increases the consistency of the behavior of the parts of the system and its organization.

According to the degree of organization, systems can be classified into well-organized, poorly organized and self-organizing.

In a well-organized system, elements and connections are clearly and unambiguously visible, and therefore the process of its functioning has a deterministic character. Such systems are, for example, low-element mechanical devices - a bicycle, a watch, etc.

In a poorly organized system, the interactions of elements become less obvious, difficult to determine, and thus the processes occurring in it will already have a random nature. The determinism of the functioning of the system gives way to stochastic regularities. A clear illustration of them can be found in the statistical processes of the interaction of molecules in a gas, which is why these systems are also called diffuse. An example of such processes are those that implement the satisfaction of customer requests - in the telephone network, at gas stations, etc.

Finally, self-organizing systems are even more unpredictable, capable of unexpected and non-trivial behavior.and adaptation to the environment. These include socio-economic systems, and in particular, catering, tourism, etc.

THEME 3

PATTERNS OF EDUCATION AND BEHAVIOR OF THE SOCIO-ECONOMIC SYSTEM

Program annotation

Patterns of system formation: purposefulness, differentiation and inconsistency of elements, compatibility of elements, integrativity and communicativeness of elements.

Patterns of system behavior: maintaining the integrity of the system, increasing the complexity and organization of the system, potential efficiency, hierarchy, adaptation, self-organization.

Reference abstract of the lecture

4.1. Patterns of formation of the system. The formation of the system occurs under certain conditions that serve as prerequisites for its emergence and preservation. Among these conditions, the following regularities can be found.

1. Purposefulness . The creation of a system pursues a specific goal, which is formed within the system. Purpose plays a fundamental role in shaping the structure, functions, organization and behavior of the system.

Noteworthy in this regard is the opinion of Henry Ford: “Firstly, the corporation should have as its goal the provision of certain services ... The most important thing is the goal pursued. In order to properly produce this or that, it is necessary to be guided by a certain goal ... ". Another classic of management theory, G. Emerson, also paid attention to the priority of the goal, who gave the goal setting the first place among the 12 performance principles he formulated.

2. Differentiation and inconsistency of elements . In the process of system formation, its elements appear as heterogeneous, different from each other, which introduces inconsistency in the relationship between them and with the system. This inconsistency follows already from the non-identity of the whole and its parts. The whole is based primarily on what the elements have in common, unites them into a system. However, the elements also have something special, specific from the features of other elements. But it is thanks to differentiation and different specialization that the elements can complement each other and contribute to the performance of common functions.

3. Element Compatibility . The functioning of the system as a whole implies not only the differentiation of its elements, but also their compatibility. The joint behavior of elements implies that they have the ability to interact. Otherwise, the coordinated behavior of the elements will be violated by the absence of some (or all) of them of links that ensure coordination.elements.

4. Integrity of elements . For the implementation of system-wide functions, the elements come into contact and combine, representing integrity. Such integration of elements becomes possible if the strength of the connections between them exceeds the strength of their interaction with the environment. Otherwise, there will be a break in internal connections, and the elements may be outside the system, jeopardizing its integrity.

5. Communication elements . The integrativity of systems does not exclude, but, on the contrary, implies the interaction of elements of open systems not only within the system, but also outside it, that is, with elements of the external environment. Through communication channels, the system can exchange resources (material and energy, labor, financial, informational, etc.) with the external environment, as a result of which the environment of the system sets the conditions for its functioning.

4.2. Regularities of system behavior.The functioning of the system is subject to certain properties that are essential and repeatable. They represent patterns of system behavior and manifest themselves in the form of trends in its development. Among them, the following are of methodological importance.

1. Preserving the integrity of the system . In the process of functioning, the system seeks to ensure its integrity due to the modernization of the elements and structure of the system, since otherwise it will face the destruction of internal connections and integrity.

2. Increasing the complexity and organization of the system . Maintaining the integrity of the system in the face of increasing disturbances inside and outside it encourages the system to respond to them by complicating, reorganizing, generating new elements and connections, which allows the system to withstand interference and maintain its ownsustainability.

3. Potential Efficiency . This regularity establishes the dependence of the limiting properties of the system on the complexity of its structure and behavior. In accordance with this, the potential capabilities of the system have their limits, and if they are exhausted, the system needs to become more complex.

4. Hierarchy. In the course of increasing the complexity of the system, the system is restructured, the links of the elements are rebuilt vertically and horizontally, and they are resubordinated, which entails a change in the degree of centralization of the system. At the same time, each level of the hierarchy exhibits different properties in relation to the higher and lower levels. In interaction with a higher level, the property of subordination is more manifested, in interaction with a lower level - the property of systemic unity.

5. Adaptations .. From the standpoint of hierarchy, the external environment has a dominant influence on the system. The desire of the system to maintain the stability of the parameters finds its expression in the patterns of adaptation. The adaptation process can proceed passively, when the system only adapts to external conditions, and actively, when the system reacts to them, responding to the feedback on its environment.

6. Self-organization . Among adaptive systems, self-adjusting and self-organizing systems are usually distinguished. If the former, in the process of adapting to perturbations, change only the way of their functioning, then the latter modernize theirstructure.

For example, self-adjusting systems, in accordance with fluctuations in demand for their services, can increase the volume of profitable services and curtail the production of unprofitable services. In contrast, self-organizing systems carry out deeper transformations in their production structure - they create new divisions and master the technology for the production of services that are beneficial to them.

Self-organization involves the accumulation of information about situations in the past and, taking into account its development, the line of further behavior of the system. Thus, it gains experience and engages in self-learning, thanks to which the system has the ability to consciously adjust its mode of operation and achieve the goal.

It should be noted that the regularity of self-organization currently remains largely mysterious for researchers and poorly understood.

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