A system is not formed. An ideal education system - what should it not be? f) inventory management

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

A common mistake in this case is further improvement of individual elements, and Not building a system from them. Within TRIZ, in this case they say that the system is incomplete and needs to be “built to completion” in order to obtain the desired system property / quality...

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

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

EXAMPLE.“...until all the knowledge necessary for the innovation on which they are based is brought together, the innovation will not become a reality, it will not take place. For example, Samuel Langley, who, according to the expectations of his contemporaries, was supposed 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 all the scientific resources of the nation at his disposal. But he preferred not to pay attention to 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 large weight of the steam engine, he could not take on board any cargo, not even a pilot. In order for the airplane to appear, a fusion of mathematics and the gasoline engine was required. Until all the necessary knowledge comes together, the countdown for the innovation based on this new knowledge to become a reality does not even begin.”

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

Rice. 1. Concept of system

“A system is a complex of interacting components.”

“A system is a set of interconnected 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 usually means that a system is a certain set of interconnected 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, consisting of interdependent parts.

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

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 intangible objects (elements, subsystems) united by some kind of connections (informational, mechanical, etc.), designed to achieve a specific goal and achieving it in the best possible way. System is defined as a category, i.e. its disclosure is carried out through identifying the main properties inherent in the system. To study a system, it is necessary to simplify it while maintaining the basic properties, i.e. build a model of the system.

System can manifest itself as an integral material object, representing a naturally determined 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, and external environment.

Property– this is the quality of the object’s parameters, i.e. external manifestations of the method by 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 and it is observed. Properties provide the ability to describe system objects quantitatively, expressing them in units of a certain dimension. The properties of system objects can change as a result of its action.

The following are distinguished: basic properties of the system :

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

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

· Presence of a specific organization, which is manifested in a decrease in the degree of uncertainty of the system compared to the entropy of the 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 connections that the element may have.

· Availability 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 set of elements; By decomposing a system into separate parts, it is impossible to know all the properties of the system as a whole.

· Emergence – 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; conversely, any change in the system affects 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 skills. Any system operates in an environment, it experiences the influence of the environment and, in turn, influences 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 that largely determines its properties.

· The system is inherent property to develop, adapt to new conditions by creating new connections, elements with their local goals and means of achieving them. Development– explains complex thermodynamic and information processes in nature and society.

· Hierarchy. Below 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 underlying levels to the higher ones. Hierarchy of the system is that it can be considered as an element of a higher order system, and each of its elements, in turn, is a system.

An important system property is system inertia, determining 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 a system to change the purpose of operation depending on the operating conditions or state of the subsystems.

· Adaptability – the ability of a system to change its structure and choose behavior options in accordance with 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 is the property of a system to implement specified functions within a certain period of time with specified quality parameters.

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

· Vulnerability – the ability to be damaged when exposed to external and (or) internal factors.

· Structurality – 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 over time.

· Availability of feedback.

Any system has a purpose and limitations. The goal of the system can be described by the target function U1 = F (x, y, t, ...), where U1 is the extreme value of one of the indicators of the quality of the system’s functioning.

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

State of the system is an instant photograph, or a snapshot of the system, a stop in its development. It is determined either through input interactions or output signals (results), or through macroparameters, macroproperties of the system. This is a set of states of its n elements and connections between them. The specification of a specific system comes down to the specification of its states, starting from its inception and ending with its death or transition to another system. A real system cannot be in any state. Her condition is subject to restrictions - some internal and external factors (for example, a person cannot live 1000 years). Possible states of a real system form in the space of system states a certain subdomain Z SD (subspace) - a set of permissible states of the system.

Equilibrium– the ability of a system, in the absence of external disturbing influences or under constant influences, to maintain its state for an indefinitely long time.

Sustainability is the ability of a system to return to a state of equilibrium after it has been removed from 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. Concept of system structure.

System structure– a set of system elements and connections between them in the form of a set. System structure means structure, arrangement, order and reflects certain relationships, the mutual position of the components of the system, i.e. its structure and does not take into account the many properties (states) of its elements.

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

Rice. 2. System structure

The concept of a system element. A-priory element- It is an integral part of a complex whole. In our concept, a complex whole is a system that represents an integral complex of interconnected elements.

Element- a part of the system that is independent 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.

Communication concept. Connection– a set of dependencies of the properties of one element on the properties of other elements of the system. Establishing a connection between two elements means identifying the presence of dependencies in their properties. The dependence of the properties of elements can be one-sided or two-sided.

Relationships– a set of two-way dependencies of the properties of one element on the properties of other elements of the system.

Interaction– a set of interrelations and relationships between the properties of elements, when they acquire the nature of interaction with each other.

The concept of the external environment. The system exists among other material or intangible 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 essence, delineating or identifying 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 the external environment.

External environment– a set of objects (systems) existing in space and time that are assumed 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.

Types of structures

Let's consider a number of typical system structures used to describe organizational, economic, production and technical objects.

Usually the concept of “structure” is associated with the graphic display of elements and their connections. 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 systems modeling tools.

Linear (sequential) the structure (Fig. 8) is characterized by the fact that each vertex is connected to two neighboring ones. When 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 connection. This increases the speed of communication and makes the structure more durable.

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

Multiply connected structure (Fig. 11) has the structure of a complete graph. Operational reliability is maximum, operational efficiency is high due to the presence of shortest paths, cost is maximum.

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

Graphovaya structure (Fig. 13) is usually used when describing production and technological systems.

Network structure (net)- a type of graph structure that represents a decomposition of the system in time.

For example, a network structure can reflect the order of operation of a technical system (telephone network, electrical network, etc.), stages of human activity (in production - a network diagram, in design - a network model, in planning - a network model, network plan, etc. .d.).

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

Hierarchical structures represent a decomposition of a 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 tree-like structures (structures "tree" type; structures on which tree order relationships are carried out, hierarchical structures with strong connections) (Figure 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 (Figure 14, b).

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 the form of hierarchical structures.

In general, the termhierarchy more broadly, it means subordination, the order of subordination of persons of lower position and rank to higher ones, it arose as the name of the “career ladder” in religion, is widely used to characterize relationships in the apparatus of government, army, etc., then the concept of hierarchy was extended to any coordinated order of objects according to subordination.

Thus, in hierarchical structures, it is only important to highlight the levels of subordination, and there can be any relationship between the levels and components within the 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.

Today I want to talk about the “ideal” education system. The voices of the dissatisfied are heard more and more often; the current state of affairs does not seem to suit anyone anymore - neither students, nor teachers, nor large customers in the form of business (unless the state is sweetly dozing or is preoccupied with other, more important matters).

I’ll start with the framework: I can’t talk about the entire education system, so we will only talk about educational processes within IT. An attempt on my part to offer something in other areas of knowledge would be either strong cunning or outright incompetence: it is unlikely that anything can be radically changed in the training of a doctor or other high-tech worker, whose activities involve a high degree of responsibility or high technological workload. Therefore, I limited myself only to those areas in which it is possible to apply the principles of self-training; where training does not require complex technical objects (like aircraft emulators for pilot training).

So, first, let’s define what “entities” (let’s call them that) in the education system and how they interact with each other in the educational process. We can safely highlight several important entities:

administrative part of the education system (hereinafter “administration”);

the state as an aggregator of many requests to the education system (hereinafter referred to as the “customer”, whose role may not necessarily be the state, but a business or a private individual).

This system can be supplemented, but perhaps there is no need to complicate it unnecessarily (for example, we will omit such an entity as “parents”; I will assume that “students” include this entity within themselves). It is quite obvious that the main vector of interactions in this system looks something like this:

In this case, interactions between non-adjacent levels are possible, but most often this does not happen. That is, the processes between the levels “students” - “teachers” are much more intense than between the levels “students” - “administration”, and there is no need to talk about the level of interaction “students” - “customer”. Is it good or bad? Both good and bad. Hierarchical schemes are successfully managed, but at the same time, problems at the bottom are sometimes poorly visible from above. And vice versa.

It is obvious that at the moment each participant (entity) of the educational process has various expectations that cannot be satisfied in the existing relationships. This naturally leads to various problems. Which ones?

"Students". Most often dissatisfied with the following:

a) a diploma (certificate of education) in itself is not valued by the “customer”, since it does not reflect the real value of a specialist;
b) the level of knowledge obtained in the system does not always correspond to at least minimally acceptable standards - the transferred knowledge is either very outdated or taught at a low level;
c) knowledge transfer processes are ineffective, since they do not take into account the psychophysical characteristics of students (“strong” and “weak” students are averaged by the system).

"Teachers". Claims made by entities of this level:

a) a huge problem for the teaching staff - dissatisfaction with the financial component of the work;
b) the issue of recent years is the deterioration in the quality of the student flow due to a decrease in the level of basic knowledge, an increase in the number of paid places (because of this, very, very weak applicants get into the system). This entails a complication of the teacher’s work (working with more gifted students is both easier and more interesting);
c) dissatisfaction with reforms in higher education - the practical effect is invisible (for example, the transition from a five-point grading system to a ten-point one).

"Administration". What doesn’t suit the layer leading the process:

a) deterioration in the quality of teaching staff, reduction in the number of employees. It is becoming increasingly difficult to attract young specialists into the system, since potentially good candidates for teaching positions go into production;
b) lack of a clear strategy for personnel reproduction.

"Customer". It seems that this is the only participant who is so far satisfied with everything in the form in which it is. At least I'd like to think so. But if you identify the “customer” as a business, he will also have something to be dissatisfied with. It seems to me that there will be two main complaints here:

a) weak “exhaust” - the number of vacancies is not covered by the existing student output volumes. As a result, this creates a shortage of personnel, which leads to a heating up of the market - wages are rising (surprise, surprise! again, such news that business doesn’t like!). My personal micro-conclusion: by investing in the education system, you can maintain the growth of wages in the industry;
b) the very quality of the “exhaust” - the modern education system provides more or less passable basic knowledge, but does not provide the required amount of knowledge on the modern technology stack;
c) business has little influence on the processes that take place in the “student” - “teacher” relationship system.

It’s clear that as a teacher (and a little bit of an administrator), I am more close and understandable to the relationship between teachers and students, as well as between teachers and administration, THAN BETWEEN WHOM AND WHOM? But the overall picture emerges quite clearly.

The overall result is this. The education system has accumulated a fairly large number of problems that are difficult to solve under the existing system.

So what exactly should be the “ideal” education system that can solve problems as they arise? I got different answers to this question!

From a student's point of view: The education system should provide the knowledge that is most in demand, a guarantee of work upon graduation, and the opportunity to put as little effort as possible into learning.

From a teacher's point of view: the system should maximize financial and moral satisfaction from work while minimizing labor costs.

From the administration's point of view: the system must be self-regulating to minimize efforts to regulate the learning process.

From the customer's point of view: the system must maximize the quantity of labor with the highest quality training for the minimum amount of money spent.

So, all participants in relationships in the educational process tend to reduce efforts to achieve results. Students, teachers and administration are inclined to reduce labor costs, and the customer is inclined to reduce financial costs. And everyone is unhappy with this situation! Students are dissatisfied with the resulting quality of education (while not wanting to expend labor effort), teachers are dissatisfied with the decrease in financial flows (while also not wanting to expend labor effort). The administration suffers from the “overregulation” of the system, since in the current situation it is not able to manage the education system. The customer is dissatisfied with the quality of knowledge and the number of specialists at the output, but at the same time is inclined to minimize financial costs.

Is it worth abandoning any of the above categories in the training system? Obviously not. Students cannot be expelled, this is clear. Does it make sense to do without teachers? Of course not (there are self-taught people who are able to study on their own - but this is not about them). The teacher function not only speeds up the learning process, but also guides it, minimizing the time spent on learning. Are we able to abandon the administration? Apparently, no, either, since the functions of the administration are regulatory and supervisory. Well, maybe try to reduce the staff of this layer as much as possible. How to refuse a customer? If there is no customer, then there is no point in training specialists.

The general conclusion is that any education system will consist of 4 layers/categories, and if we consider the “ideal” system as a reflection of the desires of each of the parties, then we will get a non-working system, where each of the categories will strive to reduce its costs. Consequently, there cannot be an “ideal” system; any construction of it will be a compromise, or the ideal system will be the one with the highest possible quality output, with optimal satisfaction of all participants in the system and minimizing the costs of its maintenance.

What can be done in this case? First of all, admit: Modern approaches to teaching are outdated!

Yes, we must admit that the system needs to be changed. How can modern approaches to organizing processes help? First of all, you need to change the structure of the system, for example, to this:

In this scheme, all participants have equal rights and can directly influence the learning process. Students can communicate with the customer, who can motivate students to study, he also has the opportunity to quickly influence the content of educational programs, teachers - to respond more sensitively to changing trends in the field of production.

What can be changed in the process of training specialists? Here are just some recommendations:

introduction of high-quality distance courses into the educational process (), however, independent development of such courses will be very expensive (according to OCW Concorcium estimates, the cost of preparing 1 hour of a course is $1000;

the use of an asynchronous model of conducting classes (students work independently, watching recorded lectures, but under the supervision of the course leader, so those who learn the material faster can move faster in their studies);

the use of mixed groups - more experienced students pass on experience to junior students, also under the supervision of the course leader. In mixed groups, the process of knowledge transfer is very fast!

use of recordings of courses, seminars, conferences in the learning process;

creation of a unified knowledge base within the country, unification of work programs, courses, assignments, etc.;

optimization of “paperwork” in the system through the introduction of a unified republican electronic document management system;

it is necessary to educate a new wave of teachers, those who can put all these elements of the system into operation, and for this it is necessary to create attractive working conditions and a fair system of payment;

increase enrollment in IT specialties, and for this we need to seriously engage in vocational guidance in high school;

invite foreign specialists to conduct classes and train their own specialists;

learn to motivate students to study;

think about introducing a unified electronic diploma (certificate) of education (http://degreed.com/about);

actively use webinars in training.

So, on the one hand, we must admit that to modernize the system it is necessary to spend a large amount of money! But with the introduction of unified unified courses, the use of electronic document management and reporting systems, and changing the concepts of interactions in the system, it is obviously possible to achieve a significant reduction in the costs of training specialists while simultaneously increasing both their quality and quantity.

In this article we will look at the definition of a system as a device made up of various structural elements. Here the issue of 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 system as a term is determined 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 often difficult to unambiguously disassemble such a mechanism, which is another reason for using the term “system”.

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

Definition of the term

There are various definitions of a 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 sciences. The content of the context about the system, the field of knowledge and the purpose of study and analysis also greatly influence the definition of this concept. The problem with exhaustive characterization lies in the use of both objective and subjective terms.

Let's look at 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, as well as related to the environment.
• A system is a set of interconnected components and parts, isolated from the environment, but interacting with it and working as a single whole.

The first definitions of a descriptive system date back to the early period of development of systems science. This terminology included only elements and a set of connections. Then they began to include various concepts, such as 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 Plato's philosophical system.
• When creating a classification.
• When creating a structure.
• When naming a set of established life norms and behavioral rules. An example is a 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, systems science, thermodynamics, system dynamics, etc.

Characterization of a system through its constituent components

The basic definitions of a system include a number of characteristics, through the analysis of which one can, in one way or another, give it a comprehensive description. Let's consider the main ones:

• The limit to dividing a system into fragments is the definition of an element. From the point of view of the aspects considered, the tasks to be solved and the goal set, they can be classified and differ in different ways.
• A component is a subsystem that is presented to us in the form of a relatively independent particle of the system and at the same time possesses some of its properties and sub-goal.
• Communication is the relationship between the elements of a system and what they limit. Communication allows you to reduce the degree of freedom of fragments of the “mechanism”, but at the same time acquire new properties.
• Structure is a list of the most essential components and connections that are little changed during the current functioning of the system. It is responsible for the presence of the main properties.
• The main concept in defining a system is also the concept of goal. Goal is a multifaceted concept that can be defined depending on the context data 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 certain patterns. The first is the presence of limitations from the general environment. In other words, this is integrativeness, which defines the system as an abstract entity with integrity and clearly defined limits 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 some may not interact in any way, but the influence in any case is 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 various parts of a system as separate systems.

Classification data

Almost all publications studying systems theory and systems analysis discuss the question of how to correctly classify them. The greatest diversity among the list of opinions about this distinction concerns the definition of complex systems. The majority of classifications are arbitrary, which are also called empirical. This means that most often authors arbitrarily use this term when they need to characterize a specific problem being solved. The distinction is most often made by defining the subject and the categorical principle.

Among the main properties, people 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 specific 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, the patterns and processes are always clearly limited, and in accordance with their origin they are distinguished: 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 associated with the issue of perceiving them as complex or simple. However, this is where the greatest amount of disagreement lies when trying to give an exhaustive list of characteristics according to which it is necessary to differentiate 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 basis of the differences and got probabilistic and deterministic. Examples of the latter are simple structures such as window shutters and machine shop designs. Complex ones are represented by computers and automation.

A probabilistic arrangement of elements in a simple form can be the toss of a coin, the movement of a jellyfish, the presence of statistical control in relation to product quality. Among complex examples of a system, we can recall the storage of reserves, conditioned reflexes, etc. Super complex forms of the probabilistic type: the concept of economics, brain structure, company, 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 connections with each other, it is necessary to determine the presence of problem-solving ability. It is important that the system has diversity that exceeds that of the problem being worked on. The second feature is that the system has the ability to create such diversity. In other words, the design of the system must be regulated so that it can change its properties in response to changes in the conditions of the problem being solved or the manifestation of disturbance.

In the absence of such characteristics in the phenomenon under study, the system will not be able to satisfy 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 general theory

The definition of a system is not only its general characteristics, but also a set of various important aspects. One of them is the concept of general systems theory, which is presented in the form of a scientific and methodological concept for studying objects that form a system. It is interconnected with such a terminological unit as the “systems 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 system objects.

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

System - this is a complete, holistic 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 systems of representations (categories), among which the main ones are:

Structural representation is associated with the identification of system elements and connections between them.

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

Macroscopic view - understanding the system as an indivisible whole interacting with the external environment.

The microscopic view is based on viewing the system as a collection of interconnected elements. It involves revealing the structure of the system.

The hierarchical representation is based on the concept of a subsystem, obtained by decomposition (decomposition) of 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 collection of subsystems at various levels, constituting a system hierarchy, which is closed from below only by elements.

The process view presupposes an understanding of a system object as a dynamic object, characterized by a sequence of its states over time.

Object cognition is the honor of the real world, which stands out and is perceived as a single 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 corresponding mutual conditionality that fall inside form a system.

Those elements that remain outside the boundary form a set called in systems theory the “system environment” or simply “environment” or “external environment”.

From these considerations it follows 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, being the leading component of this influence.

Depending on the impact on the environment and the nature of interaction with other systems, the functions of systems can be arranged in increasing 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, as a supersystem of a lower order system (subsystem). For example, the “production workshop” system is included as a subsystem in a higher-ranking system - “company”. 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 and a certain degree of freedom.

Component - any part of the system that enters into certain relationships 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 interconvertible; a system can be considered as an element of a higher order system (metasystem), and an element, in in-depth analysis, as a system. The fact that any subsystem is simultaneously a 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) and the conditions for its functioning. In this case, the elements of the system are studied from the point of view of their organization into a single whole and their influence on the functions of the system as a whole.

At the micro level, the main ones are the internal characteristics of the system, the nature of the interaction of elements with each other, their properties and operating conditions.

To study the system, both components are combined.

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

The structure of a system is understood as a stable set of relationships 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 manifestations of the object.

Connections are elements that directly interact 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 because of the presence of connections between its elements, i.e., in other words, the connections express the laws of the functioning of the system. Connections are distinguished by the nature of the relationship as direct and inverse, 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.

Feedbacks, Basically, they perform informative functions, reflecting changes in the state of the system as a result of control actions 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, and 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 element. Here, this signal, containing information about the work performed by the control object, is compared with a signal that specifies the content and volume of work (for example, a plan). If there is a discrepancy between the actual and planned state of work, measures are taken to eliminate it.

The main functions of feedback are:

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

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

synthesizing external and internal disturbances that tend to bring the system out of a state of stable equilibrium, reducing these disturbances to deviations of one or more controllable quantities (for example, developing control commands for the simultaneous emergence 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 resources causes complex changes in the activities of various organizations, changes the final results of their functioning, and requires changes in the production and economic process through impacts that cannot be described using analytical expressions.

Violation of feedback loops in socio-economic systems for various reasons leads to serious consequences. Individual local systems lose the ability to evolve and sensitively perceive emerging new trends, long-term development and scientifically based forecasting of their activities for a long period of time, and 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 feedback links, which in them, as a rule, are long, pass through a number of intermediate links, and their clear viewing is difficult. The controlled quantities themselves are often not clearly defined, and it is difficult to establish many restrictions imposed on the parameters of the controlled quantities. The actual reasons for controlled variables going beyond the established limits are also not always known.

Deterministic (hard) coupling, as a rule, unambiguously defines cause and effect and provides a clearly defined formula for the interaction of elements.Probabilistic (flexible) communication -Defines implicit and indirect dependencies between elements. Probability theory offers a special mathematical apparatus for studying these connections, called correlation analysis.

Criteria are signs by which the compliance of the functioning of the system with its purpose is assessed under given restrictions.

The effectiveness of the system is the relationship between the target result of operation and the one actually realized.

Often there are restrictions on the input and output - ensures compliance between the output of the system and the input requirements of 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 the set of essential properties that the system possesses at the current moment.

3. Basic properties of systems (6 properties).

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

From the definition of a system it follows that the main property is integrity or unity, ensured by the relationships between 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. The underlying principle is the opposite of reductionism, which states that a whole can be studied by dividing it into parts and then, by determining the properties of the parts, determining the properties of the whole.

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

Integrity and emergence are integrative properties of the system.

Integrity lies in the fact that each component 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). An indispensable part of systems is their components, namely those structural formations that make up the whole and without which it is not possible.

Functionality- this is the 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 orderliness of the system, a certain set and arrangement of elements with connections between them. There is a relationship between the function and structure of a system, as between the philosophical categories of content and form. A change in content (functions) entails a change in form (structure), but also 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 (surrounding), i.e. with other systems with which it comes into contact or enters into certain relationships. The process of purposefully changing the state of a system over time is called behavior. Unlike control, when a change in the state of the system is achieved through 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 one at that).

The fundamental property of systems is stability, i.e. the ability of the system to withstand external disturbances. The lifespan of the system depends on it. Simple systems have passive forms of stability: strength, balance, adjustability, 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 through their replacement or duplication, and survivability - as 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 preserve, improve or acquire new qualities in conditions of changing external environment. A prerequisite for the possibility of adaptation is the presence of feedback connections.

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

Classification called division into classes according to the most essential characteristics. Under class is understood as a collection of objects that have certain characteristics of commonality. A characteristic (or a set of characteristics) is the basis (criterion) of classification.

A system can be characterized by one or more characteristics and, accordingly, a place can be found in various classifications, each of which can be useful when choosing a research methodology. Typically, the purpose of classification is to limit the choice of approaches to displaying systems and 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:created by humanity for its needs or formed as a result of purposeful efforts. Artificialare divided into technical (technical and economic) and social (public).A technical system is designed and manufactured by a person for a specific purpose.

TO social systemsinclude various systems of human society.

The identification of systems consisting of technical devices alone is almost always conditional, since they are not capable of generating their own state. These systems act as parts of larger organizational and technical systems that include people.

An organizational system, for the effective functioning of which a significant factor is the way of organizing the interaction of people with a technical subsystem, is calledman-machine system. Examples of human-machine systems: car - driver; airplane - 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. Distinctive 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 a 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 based on the specific purpose of the system. The structure also determines the ability of the system to redistribute functions in the event of complete or partial waste of individual elements, and, consequently, the reliability and survivability of the system for the 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 their source of origin, since their primary source is objectively existing reality.
Abstract systems shareto direct display systems(reflecting certain aspects of real systems)and systems of generalizing (generalizing) display.The first includes mathematical and heuristic models, and the second includes 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 that interacts with its environment. All real systems are open. When describing the structure of such systems, they try to divide external communication channels 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 identify and include only significant connections in the system. The unimportant ones 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, input channels exist, but the influence of the environment is constant and completely known in advance. In this case, such influences are attributed directly to the system, which allows us to consider it as closed.

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. Serves to perform the simplest functions; hierarchical levels cannot be distinguished in them. A distinctive feature is the determinism (clear definition) of the nomenclature, the number of elements and internal and external connections.

Complex - contain a large number of elements and internal connections, and are characterized by structural diversity. Performs a complex function or 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 taking into account uncertainty.

A model is a certain description (mathematical, verbal, etc.) of a system or subsystem, reflecting the group and its property.

A system is called complex if in reality the following signs of complexity are significantly manifested:

Structural complexity

Basic concepts of connections:

Structural

Hierarchical

Functional

Causal (cause and effect)

Information

Spatiotemporal

Difficulty functioning (behavior)

The complexity of choosing behavior. In multi-alternative situations, the choice of behavior is determined by the goal of the system.

Complexity of development.

Determined by the characteristics of evolutionary or stochastic processes.

These signs 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 significant for it. The number of its subsystems is very large, and its composition is heterogeneous. When analyzing and synthesizing large and complex systems, decomposition and aggregation procedures are fundamental.

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

Automatic - react uniquely 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 discrimination criteria and flexible reactions to external influences. Can adapt to influences. They have characteristics of diffuse systems, stochastic behavior and instability of parameters and processes. Capable of slightly changing the structure. For example: biological organizations, collective behavior of people, etc. If its stability exceeds external influences, thenthese are predictive systems. That is, they can foresee the future course of events.

Transforming systems- imaginary complex systems at the highest level of complexity, not bound by the constancy of existing media. They can change material media and their structure while maintaining 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 plays a dominant (central) role, which determines its functioning.

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

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

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.

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

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

Qs ≠ ∑Qi

the properties of the system (the 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 elements combined into a system, as a rule, lose some of their properties inherent in them outside the system, i.e. the system seems to suppress a number of properties of elements. But, on the other hand, elements, once in the system, can acquire new properties.

Let us turn to the pattern that is dual in relation to the pattern of integrity. It is called physical additivity, independence, summation, isolation. The property of physical additivity is manifested in a system that seems to have broken down into independent elements; then it becomes fair

Qs = ∑Qi

In this extreme case, it is no longer possible to talk about the system.

Let's 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.

Integrative - This term is often used as a synonym for integrity. However, some researchers highlight this pattern as independent, trying to emphasize the interest not in the external factors of the manifestation of integrity, but in the deeper reasons that determine the emergence of this property, in the factors that ensure the preservation of integrity.

Integrative are system-forming, system-preserving factors, among which an important role is played by the heterogeneity and inconsistency of elements (studied 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 laws also characterizes the interaction of the system with its environment - with the environment (significant or essential for the system), the supersystem, and subordinate systems.

Communication skills- This pattern 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 (metasystem - a higher order system that specifies the requirements and limitations of the studied system), subsystems (lower-lying, 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 constructing the entire world and any system isolated from it.

Hierarchy - The laws of hierarchy or hierarchical ordering were among the first laws of systems theory that L. von identified 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 directing influence on the lower level subordinate to it, and this influence is manifested in the fact that subordinate members of the hierarchy acquire new properties that they did not have in an isolated state (confirmation of the position about the influence of the whole on the elements given above), and as a result of the appearance of these new properties, a new, different “look of the whole” is formed (the influence of the properties of the elements on the whole). The new whole that arises in this way acquires the ability to carry out 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 lower levels)

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

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

The problem of system feasibility is the least explored. Let's consider some of the patterns that help to understand this problem and take it into account when determining the principles of design and organization of the functioning of control systems.

Equifinality- This pattern characterizes, as it were, the maximum capabilities of the system. L. von Bertalanffy, who proposed this term, defined equifinality as “the ability, in contrast to the state of equilibrium in closed systems completely determined by initial conditions, ... to achieve a time-independent state that does not depend on its initial conditions and is determined exclusively by the parameters of the system " In accordance with this pattern, the system can achieve the required final state, independent of time and determined exclusively 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 diversity" -For the first time in systems theory, U.R. drew attention to the need to take into account the ultimate feasibility of a system when creating it. Ashby. He formulated a pattern known as the law of “necessary diversity.” For decision-making problems, the most important is one of the consequences of this pattern, which can be simplified by the following example.

When a researcher (DM - decision maker, observer) N is faced with 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 researcher’s task 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 diversity in N can reduce the diversity created in D; only diversity can destroy diversity.”

In relation 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 (or at least equal) to the diversity of the controlled object Vou:

Vsu > Vou.

The following ways to improve management as production processes become more complex are possible:

an increase in Vsu, which can be achieved by increasing the number of management staff, improving their qualifications, mechanization and automation of management work;

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

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

self-organization of control objects by limiting controlled parameters through the creation of self-regulating units (shops, areas 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 the principles of their changes over time when modeling systems has become increasingly realized, for the understanding of which the patterns discussed 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 development of organizational systems and complex technical complexes it is difficult to determine these periods. Managers 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 pattern of historicity, and that this pattern is as objective as integrity, hierarchical ordering, etc. At the same time, the pattern of historicity can be taken into account not only passively , recording 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 isAmong the main features of self-organizing systems with active elements are the ability to resist entropic (entropy in this case is the degree of uncertainty, unpredictability of the state of the system and the external environment) trends, the ability to adapt to changing conditions, transforming its structure if necessary, etc. These outwardly manifested abilities are based on a deeper pattern, based on the combination in any real developing system of two contradictory tendencies: on the one hand, for all phenomena, including developing, open systems, the second law of thermodynamics (“second law”) is valid. , i.e. the desire to increase entropy; and on the other hand, negentropic (opposite to entropic) tendencies underlying evolution are observed.

Important results in understanding the laws of self-organization were obtained in studies that belong to the developing science called synergetics.

10. What is synergetics? What is it used for? Give a brief description of the 9 main principles of the synergetic approach.

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

many heterogeneous components;

activity (purposefulness) of components;

many different, parallel relationships between components;

semiotic (weakly formalized) nature of relationships;

cooperative behavior of components;

openness;

distribution;

dynamism, learning ability, evolutionary potential;

uncertainty of environmental parameters.

A special place in synergetics is occupied by the issues of spontaneous formation of ordered structures of various natures in interaction processes when the initial systems are in unstable states. Following the scientist I. Prigogine, 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 the sequential passage of critical areas (bifurcation points (bifurcation, branching)). Near the bifurcation points, a sharp increase in fluctuation is observed (from the Latin fluctuatio - fluctuation, deviation). The choice of development after bifurcation is determined at the moment of instability. Therefore, the bifurcation zone is characterized by fundamental unpredictability - it is unknown whether the further development of the system will become chaotic or a new, more ordered structure will be born. Here the role of uncertainty increases sharply: randomness at the input in a non-equilibrium situation can lead to catastrophic consequences at the output. At the same time, the very possibility of spontaneous emergence of order from chaos is the most important moment in the process of self-organization in a complex system.

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

N. Bohr's principle of complementarity.In complex systems, there is a need to combine various models and methods of description that previously seemed incompatible, but now complement 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).

The principle of incompatibility L. Zadeh. As the complexity of a system increases, 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.Complex systems require a transition from dealing with uncertainty to managing uncertainty. Various types of uncertainty must be deliberately introduced into the model of the system under study, since they serve as a factor favoring innovation (system mutations).

The 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, in such systems, modeling partial knowledge and ignorance plays an important role.

Principle of correspondence. The language used to describe a complex system must correspond to the nature of the information available about it (the level of knowledge or uncertainty). Exact logical-mathematical and syntactic models are not a universal language; loose, approximate, semiotic models and informal methods are also important. The same object can be described by a family of languages ​​of varying severity.

The principle of diversity of development paths. The development of a complex system is multivariate and alternative; there is a “spectrum” of paths for its evolution. The critical turning point of uncertainty about the future development of a complex system is associated with the presence of bifurcation zones - “branching” of possible paths of 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 presupposes a kind of conjunction of order and chaos.

Oscillatory principle(pulsating) evolution. The process of evolution of a complex system is not progressive, but cyclical or wave in nature: it combines divergent (increasing diversity) and convergent (collapse of diversity) trends, phases of the emergence of order and the maintenance of order. Open complex systems pulsate: differentiation is replaced by integration, scattering by rapprochement, weakening connections by their strengthening, etc.

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

11. Name 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, cyberneticists, and observation of the processes of justification and structuring of goals in specific conditions made it possible to formulate some general principles and 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 “goal” allows us to conclude that when formulating a goal, we must 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 it with with its help, 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.

Dependence of the goal on external and internal factors- When analyzing the reasons for the emergence and formulation of goals, it is necessary to take into account that the goal is influenced by both factors external to the system (external requirements, needs, motives, programs) and internal factors (needs, motives, programs of the system itself and its elements, performers goals); Moreover, the latter are the same factors that objectively influence the goal-setting process as external ones (especially when using the concept of goals in management systems as a means of inducing action).

Manifestation of the pattern of integrity in the structure of goals -In a hierarchical structure, the pattern 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 higher-level goal 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) need to be investigated 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 may propose 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 of representing goals in organizational management systems is 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 goal structures “from below” - morphological, linguistic, thesaurus, terminal approach ; in practice, these approaches are usually combined;

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

in a hierarchical structure, as we move from the top level to the bottom, there is a shift in the “scale” discussed 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 implementation, while at the upper levels of the hierarchy, the indication of the criteria can either be expressed in general requirements (for example, “increase efficiency”), or are not included at all in the statement of the goal;

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

And a few more important laws.

Law of simplicity of complex systems- It is implemented, survives, and the version of the complex system that has the least complexity is selected. The law of simplicity of complex systems is implemented by nature in a number of constructive principles:

Occam,

hierarchical modular construction of complex systems,

symmetry,

symmorphosis (equal strength, homogeneity),

field interaction (interaction through the carrier),

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

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

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

Law of equivalence of options for constructing complex systems- As the complexity of the system increases, the share of options for its construction that are close to the optimal option increases.

Onsager's Law maximizing the decrease in entropy - If the number of all possible forms of process implementation, consistent with the laws of physics, is not unique, then the form in which the entropy of the system grows most slowly is realized. 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 functional description of systems? Why and how is this done? Explain the general formula for the functional description of any dynamic system.

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

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

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

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

A functional description (functional model) must create the correct orientation regarding the external connections of the system, its contacts with the outside world, and the directions of its possible change.

The functional description proceeds from the fact that every system performs certain functions: it simply exists passively, serves as an area of ​​habitat for other systems, serves systems of a higher order, and serves as a means for creating more advanced systems.

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

In many ways, the assessment of the functions of a system (in an 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 functions describing the internal processes of the system, or by a qualitative functional (ordering in terms of “better”, “worse”, “more”, “less”, etc.)

A functional that quantitatively or qualitatively describes the activity of a system is called an efficiency functional.

Functional organization can be described:

algorithmically,

analytically,

graphically,

tabular,

through operating time diagrams,

verbally (verbally).

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

must be open and allow for 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 at any level.

When describing a system, we will consider it as a structure into which something (matter, energy, information) is introduced at certain moments in time, and from which something is withdrawn at certain moments 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 moments in time, x is the set of instantaneous values ​​of input influences, C = (c: T → x) is the set of permissible input influences; Q - set of states; y - set of output values; Y = (u: T → y) - set of output quantities; φ = (T×T×T×c → Q) - transition state function; η:T×Q → y - output mapping; c - segment of input influence; u is a segment of the output value.

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

The disadvantage of this description is that it is not constructive: it is difficult to interpret and apply in practice. A functional description should reflect such characteristics of complex and poorly understood systems as parameters, processes, hierarchy.

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

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 present this dependence in explicit form, and the practical value of such a representation is insignificant due to its multidimensionality and multiplicity. A rational way to form a functional description is to use a multi-level hierarchy of descriptions in which the description of a higher level will depend on generalized and factorized variables of a 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 significantly less than the number of variables on which the processes depend. This method of description makes it possible to build a bridge between the properties of elements interacting with the environment (lower-level subsystems) and the efficiency of the system.

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

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

active counteracting environmental parameters directly directed against the system to reduce its efficiency - b1, b2, ..., bk, ..., bK;

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

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

The environment has direct contact with subsystems of lower levels, influencing through them subsystems of higher levels of the hierarchy, so Fi* = Fi*((bk), (cl), (dp)). By constructing a hierarchy (parameters of the β-th level - processes of the (β-1) level - parameters of the (β-1) level), it is possible to connect the properties of the environment with the efficiency of the system.

System parameters (Qj) can change when the environment changes; they depend on the processes in the system and are written in the form of 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 a set of parameters up to level b:

Q = (Q(1), Q(2), ... Q(β)).

The state can remain constant for a certain time interval T.

Processes (Fi(2)) cannot be detected at the system output. These are second-level processes that depend on the parameters Q(2) of the system subsystems (second-level parameters). And so on.

The following hierarchy of description is formed: efficiency (a finite set of functionals) - processes of the first level (functions) - parameters of the first level (functionals) - processes of the second level (functions) - parameters of the second level (functionals), etc. At some level, our knowledge of the functional properties of the system is exhausted, and the hierarchy breaks down. 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 upper level of the hierarchy, so it is often possible to limit ourselves to a description of the form ((Ei), (ψS), (Fi(1)), (Qj(1)), (bk), (cl), (dp)). The number of hierarchy levels depends on the required accuracy of representation of input processes.

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

The method of generalized analytical functional description of systems was discussed above. Very often, when analyzing and synthesizing systems, a graphical description is used, the varieties of which are:

system function tree,

IDEF0 functional modeling standard.

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

target function;

basic functions of the system;

additional system functions.

The target function of the system corresponds to its main functional purpose, i.e. target (main) function - reflects the purpose, essence and raison d'être 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 the conditions for performing the target function (reception, transmission, acquisition, storage, issue).

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

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

The formulation of the function inside the vertices must include 2 words: a verb and a noun “Do what”.

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

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

Formation of a function tree represents the process of decomposition of the target function and a set of basic and additional functions into more elementary functions, implemented at subsequent levels of decomposition.

Moreover, each of the functions of a specifically taken i-th level can be considered as a macro-function 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 principles of decomposition, but is presented not as a tree, but as a set of diagrams.

14. Graphic methods of functional description of systems. IDEF0 methodology. 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 the most general description of the system is presented, and the base represents many more detailed descriptions.

IDEF0 methodology is built on the following principles:

Graphic description of the simulated processes. The graphical language of Blocks and Arcs IDEF0 Diagrams displays operations or functions as Blocks, and the interaction between the inputs/outputs of operations entering or leaving a Block as Arcs.

Conciseness. By using a graphical language for describing processes, accuracy of description is achieved on the one hand, and brevity on the other.

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

The Diagram must have at least 3 and no more than 6 functional Blocks.

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

Diagrams must have a related interface when the Block numbers, Arcs and ICOM codes have a single 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.

For each functional Block, at least one control Arc is required.

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

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

The model context delineates the boundaries of the system being modeled and describes its relationships 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. Moreover, all interactions in the model are considered precisely from the point of view of achieving the set goal.

Within the IDEF0 methodology, the system model is described using Graphical IDEF0 Diagrams and refined through the use of FEO, Text and Glossary Diagrams. Moreover, the model includes a series of interconnected Diagrams that divide a complex system into its component parts. Higher level diagrams (A-0, A0) are the most general description of the system, presented in the form of separate Blocks. The decomposition of these Blocks allows us to achieve the required level of detail in the system description.

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 connections 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.

During further modeling, Block 0 is decomposed into 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 presentation.

As a result, the names of functional Blocks and interface Arcs, which 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 Level Diagram, the real "working top or structure" is the A0 Diagram because it is a refined expression of the model's point of view. Its content shows what will be considered next, limiting subsequent levels within the scope of the project goal. The lower levels clarify the content of 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 the system. Their actions are written verb + object of action + object

for example, “develop a work schedule.”

Arcs represent information or material objects that are necessary to perform a function or appear as a result of execution. The object can be: Documents, physical materials, tools, machines, information, organizations and even subsystems. The location where the arc connects to the block determines the type of interface. Comments on the arc are formulated in the form of a noun phrase that answers the question “what.” The blocks are arranged on the diagram according to the degree of the author, depending on the degree of the author. A dominant block is the block whose execution influences the control of the maximum number of blocks. The dominant block is located in the upper left corner, the least important - in the lower right.

Important!

The arrangement of blocks does not determine the time dependence of the operation!

See fig. 1

Management relationship.

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 1st.

Login feedback.

The relationship between output and mechanism. A rare type of communication used in preparatory operations.

Example: create an idef model for the control department to assess the effectiveness of the management and functioning of the library. see Figure 2. Block A0, reflecting the target function. Then, in Figure 3, the A0 diagram 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.

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

The goals of structural analysis are:

development of rules for symbolic display of systems;

assessment of the quality of the system structure;

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

developing a conclusion about the optimal structure of the system and recommendations for its further improvement.

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

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

homogeneous (elements of the same type);

heterogeneous (different types of elements);

mixed.

Sameness does not mean complete identity and only determines the proximity of basic properties.

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

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

Sometimes the elemental composition cannot be determined - it is uncertain.

An important feature of morphology is the purpose (properties) of the elements. The elements are distinguished:

informational;

energy;

real

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

Information elements are designed to receive, remember (storage), transform and transmit information. The transformation may consist of changing the type of energy that carries information, changing the method of encoding (representing in some symbolic form) information, compressing information by reducing redundancy, making decisions, etc.

There are reversible and irreversible transformations of information.

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

Energy conversion consists of 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 energy conversion process naturally requires information.

The process of converting 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 general, 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 significantly depend on the nature of the connections between the elements. The concept of communication is included in any definition of a system. It simultaneously characterizes both the structure (statics) and functioning (dynamics) of the system. Connections ensure the emergence and preservation of the structure and properties of the system. Information, material and energy connections are distinguished, defining them in the same sense in which the elements were defined.

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

The connection is characterized by:

direction,

by force,

view.

Based on the first two characteristics, connections are divided into directed and undirected, strong and weak, and by nature - subordination, generation (genetic), equal and control connections.

Some of these connections can be broken down in even more detail. For example, connections of subordination on the “genus-species”, “part-whole” connections; 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 to transfer 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 throughput and reliability.

A very important role, as we already know, is played by feedback connections - they are the basis for self-regulation and development of systems, adapting them to changing conditions of existence. They mainly serve to control processes and the most common are information feedbacks.

Neutral connections do not relate to the functional activity of the system; they are unpredictable and random. However, neutral connections can play a certain role in adapting the system, serve as an initial resource for the formation of direct and feedback connections, and serve as a reserve.

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

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

multiply connected,

hierarchical,

mixed.

The most stable are deterministic structures in which relations are either constant or change over time according to deterministic laws. Probabilistic structures change over 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 characteristic.

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 relationships of coordination and subordination.

Coordination expresses the ordering of system elements “horizontally”. Here we are talking about the interaction of components of one level of the organization.

Subordination is a “vertical” ordering of subordination and subordination of components. Here we are talking about the interaction of components at different levels of the hierarchy.

Hierarchy (hiezosazche - sacred power, Greek) is the arrangement of the parts of the whole in order from highest to lowest. The term “hierarchy” (multi-stage) defines the ordering of system components by degree of importance. Between the levels of the structure hierarchy there may be a relationship of strict subordination of the components of the underlying 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 necessarily have to exist between the levels of a hierarchical structure. Connections can also take place within the same hierarchy level. An underlying component can be subordinate to several components of a higher level - these are hierarchical structures with weak connections.

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

There are strictly and non-strictly hierarchical structures.

A system of strict hierarchical structure has the following features:

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

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

the connection exists only between components belonging to two adjacent levels, with lower-level components connected only to one higher-level component, and each higher-level component to at least two lower-level components. Fig.1

Rice. 2.

Figure 1 shows a graph of a strictly hierarchical structure, and Figure 2 shows a graph of a non-strict hierarchical structure. Both structures are three-level.

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

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

Functionally, hierarchical structures are more economical.

For non-hierarchical structures, there are no components that are only managerial 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 deterministic interaction with any subsystem;

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

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

There can be more than one leading subsystem; with several leading subsystems, a main leading subsystem is possible. The subsystem of the highest level of the hierarchical structure must simultaneously be the main leading one; if this is not the case, then the supposed 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. The structure can change without converting a class 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 a higher-level subsystem. As a result of this, the higher-level subsystem is replaced by the leading subsystem, or merges with it, or the hierarchical structure is transformed into a non-hierarchical (mixed) one.

Non-hierarchical structures without leaders are called equilibrium. Most often, multiply connected structures are in equilibrium. Equilibrium does not mean the component-wise identity of metabolism; we are talking only about the degree of influence on decision-making.

A feature of hierarchical structures is the absence of horizontal connections 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 important. 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 influencing other subsystems and systems, including the environment, with matter or energy),

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

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

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

In set-theoretic language, the 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, the depth of 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:

Compound:

homogeneous,

heterogeneous,

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

uncertain.

Element properties:

informational,

energy,

information and energy,

material-energy,

uncertain (neutral).

We will distinguish in the set V:

Purpose of connections:

informational,

real,

energy.

Nature of connections:

straight,

reverse,

neutral.

We will distinguish in d:

Structure stability:

deterministic,

probabilistic,

chaotic.

Formations:

hierarchical,

multiply connected,

mixed,

transforming.

We will distinguish in the set K:

Songs:

weak,

with effector subsystems,

with receptor subsystems,

with reflexive subsystems,

full,

undefined.

The morphological description, like the functional one, is built on a hierarchical (multi-level) principle through sequential decomposition of subsystems. The levels of system decomposition, the levels of the hierarchy of functional and morphological descriptions must coincide. A morphological description can be performed by sequential division 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 division or a small number of divisions. 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 communication between elements and the communication capacity. It can be proven that the set of elements of the structure 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 advisable to introduce a metric in the structural space.

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

Structural diagrams- Formation of the structure is part of the solution to the general problem of describing the system. The structure reveals the overall configuration of the system rather than defining the system as a whole.

If we depict the system as a set of blocks that carry out certain functional transformations and connections between them, we obtain 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 device designed as a separate whole. Division into blocks can be carried out based on the required degree of detail in the description of the structure, the clarity of the display in it of the features of the functioning processes inherent in the system. In addition to functional ones, the block diagram may include logical blocks that allow the nature of operation to be changed depending on whether certain predetermined conditions are met or not.

Structural diagrams are visual and contain information about a large number of structural properties of the system. They can easily be clarified and specified, during which there is no need to change the entire diagram, but rather replace its individual elements with structural diagrams that include not one, as before, but several interacting blocks.

However, a structural diagram is not yet a model of structure. It is difficult to formalize and is more of a natural bridge that facilitates the transition from a meaningful description of a system to a mathematical one, rather than a real tool for the analysis and synthesis of structures. Rice. - Example of a block diagram

Graphs - The relationships 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 the set of vertices, R is the set of edges (or arcs of the graph), P is the incidence predicate of vertices and edges of the graph. Р(x, y, r) = 1 means that 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, called in this case adjacent. If the graph is marked, then the edge is specified by the pair (i,j), where i and j are the numbers of adjacent vertices. Obviously, the edge (i,j) is incident to vertices i and j, and vice versa.

If all the edges of a graph are given by ordered pairs (i, j), in which the order of 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 in the form of diagrams in which vertices are displayed as points (circles, rectangles), and edges are shown as segments connecting adjacent vertices. An oriented edge is specified by a segment with an arrow.

The use of diagrams is so widespread that when we talk about a graph, we 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 connections; the sign in front of 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 brain's neural connections is not felt and does not affect behavior. There may also be unnecessary redundancy, which is depicted in the structure graph as loops.

18. Structure of system analysis. Basic solution 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, a problem of practice is identified as a discrepancy between the existing state of affairs and the required one. To solve the problem, a systemic study (decomposition, analysis and synthesis) of the system is carried out, eliminating the problem. During the synthesis, the analyzed and synthesized systems are assessed. The implementation of the synthesized system in the form of a proposed physical system allows us to assess the degree to which the practical problem has been removed 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 obvious: a 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 decomposition stage, which provides a general representation of the system, the following is carried out:

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

Isolation of a system from the environment (division into system/non-system) according to the criterion of participation of each element under consideration in the process leading to a result based on 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 relationships between elements) decomposition of the system.

The depth of decomposition is limited. Decomposition must stop if it is necessary to change the level of abstraction - to represent 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 a change in the level of abstraction has occurred. This means going beyond the goal of studying the system and, therefore, causes the cessation of decomposition.

In automated methods, model decomposition to a depth of 5-6 levels is typical. Usually one of the subsystems is decomposed to this depth. The functions that require this level of detail are often very important, and their detailed description provides clues to the operation of the entire system.

General systems theory has proven that most systems can be decomposed into basic subsystem representations. 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 unambiguous correspondence between the law of functioning of subsystems and the algorithm and its implementation. Therefore, several options (or one option, if the system is displayed in the form of a hierarchical structure) of the system decomposition are formed.

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 basis for the division into functional subsystems is the commonality of functions performed by groups of elements.

Life cycle decomposition. A sign of the identification of subsystems is a change in the law of functioning of subsystems at different stages of the life cycle of the system “from birth to death.” It is recommended to use this strategy when the goal of the system is to optimize processes and when successive stages of transforming inputs into outputs can be defined.

Decomposition by physical process. A sign of identifying subsystems is the steps of executing the algorithm for the functioning of the subsystem, the stages of changing states. Although this strategy is useful in describing existing processes, it can often result in an overly coherent description of the system that does not fully take into account the constraints imposed by the functions on each other. In this case, the control sequence may be hidden. This strategy should only be used if the purpose of the model is to describe the physical process itself.

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

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

Functional and structural analysis of the existing system, which allows us to formulate the requirements for the system being created. It includes clarification of the composition and laws of operation of elements, algorithms for functioning and mutual influence of subsystems, separation of controlled and uncontrollable characteristics, setting the state space Z, setting the parametric space T in which the behavior of the system is specified, 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, 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, direct evaluation and analysis of the obtained assessments.

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

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

Development of a model of the required system (selection of mathematical tools, 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 a system that solves the problem.

Synthesis of system parameters that solve the problem.

Evaluation of variants of the synthesized system (justification of the evaluation scheme, implementation of the model, conducting an evaluation experiment, processing of evaluation results, analysis of results, selection of the best option).

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

An assessment of the extent to which the problem has been resolved is carried out upon completion of the system analysis.

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

19. 9 stages of forming a system representation.

Stage 1. Identification of the main functions (properties, goals, purpose) of the system. Formation (selection) of basic subject concepts used in the system. At this stage we are talking about understanding the main outputs in the system. This is the best place to start researching it. The type of output must be determined: material, energy, information, they must be related to some physical or other concepts (production output - products (which?), 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 occurs, 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 connections. Such information should be presented and studied using structural or object-oriented methods of systems analysis, where, for example, the presence of a predominantly sequential or parallel nature of the connection of parts, mutual or predominantly unilateral direction of influences between parts, etc. is revealed. Already at this stage, attention should be paid to the so-called system-forming factors, i.e. on those connections and interdependence that make a system a system.

Stage 3. Identification of the main processes in the system, their role, conditions for implementation; identification of stages, leaps, changes in states in functioning; in systems with control - identifying 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, ensuring the flow of processes, as well as the conditions for the beginning and end of processes are considered. It is determined whether the processes are controllable and whether they contribute to the system’s implementation of its 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 connected. Identifying the nature of these connections. 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 impacts are directed. Here it is 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 operating features of the system. In general, this stage allows us 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 directly work. If we are talking about a system that needs to be studied in order to deeply study, improve, and manage it, 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 connections important for the purposes of consideration. Their assignment to the hierarchy structure in the system. Ranking of elements and connections 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 knowledge “inside” a sufficiently complex system for a person operating it entirely. Only the specialist responsible for its individual parts will have more in-depth knowledge about the system (stage 7). For a not too complex object, the level of stage 7 - knowledge of the entire system - is achievable for one person. Thus, although the essence of stages 6 and 7 is the same, in the first of them we are limited to the reasonable amount of information that is available to one researcher.

With in-depth detail, it is important to highlight the elements (modules) and connections that are essential for consideration, discarding everything that is not of interest for the purposes of the study. Cognizing a system not always involves only separating the essential from the unimportant, but also focusing on the more essential. The detailing should also affect the connection between the system and the “non-system”, already considered in stage 4. At stage 7, the set of external connections is considered so clear that we can talk about a thorough knowledge of the system.

Stages 6 and 7 summarize the overall, holistic study of the system. Further stages 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 an understanding of why they are exactly like that or should be exactly like that in the aspect 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 a 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 better use, and sometimes restructuring the structure and hierarchy of connections.

The main uncertainties in a stochastic system are considered to be explored at stage 5. However, indeterminism is always present in a system that is not intended to operate under conditions of the random nature of inputs and connections. Let us add that taking into account uncertainties in this case usually turns into a study of the sensitivity of the most important properties (outputs) of the system. Sensitivity refers to the degree to which changes in inputs influence changes 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 goal-directed and other controlled systems, this stage is of great importance. The main controlling factors were clarified when considering stage 3, but there it was in the nature of general information about the system. To effectively introduce controls or study their effects on system functions and processes requires in-depth knowledge of the system. That is why we are talking about control analysis only now, after a comprehensive review of the system. Let us recall that control can be extremely diverse in content - from commands from a specialized computer control to ministerial orders.

However, the possibility of a uniform consideration of all targeted interventions in the behavior of the system allows us to speak not about individual management acts, but about a management system that is closely intertwined with the main system, but is clearly distinguished in functional terms.

At this stage, it becomes clear where, when and how (at what points of the system, at what moments, in what processes, jumps, selections from the population, logical transitions, etc.) the control system influences the main system, how effective and acceptable it is and conveniently implementable. When introducing controls in the system, options for converting inputs and constant parameters into controlled ones must be explored, acceptable control limits and methods for their implementation must be determined.

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

Target

Basic Function 2

Basic Function 1

Vsp. function 2

Vsp. function 1

Vsp. function 3

Vsp. function 1

Vsp. function 2

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