In the general systemic features of Fr. Element incoming Signal Event-Fact outgoing Signal- Control structure incoming Signal Concept outgoing Signal. The functioning of the formed system occurs at two levels

1. The purpose of the course “Fundamentals of systems analysis”. Definitions of terms “System analysis, systematicity”. Purpose of system analysis (SA)

There are different points of view on the content of the concept of “system analysis” and the scope of its application. Studying various definitions of system analysis allows us to distinguish four interpretations of it.

The first interpretation considers system analysis as one of the specific methods for selecting the best solution to a problem, identifying it, for example, with analysis based on the cost-effectiveness criterion.

This interpretation of system analysis characterizes attempts to generalize the most reasonable methods of any analysis (for example, military or economic) and to determine the general principles of its implementation.

In the first interpretation, systems analysis is, rather, “analysis of systems”, since the emphasis is on the object of study (the system), and not on systematic consideration (taking into account all the most important factors and relationships that influence the solution of the problem, using a certain logic of searching for the best decisions, etc.)

In a number of works covering certain problems of system analysis, the word “analysis” is used with such adjectives as quantitative, economic, resource, and the term “system analysis” is used much less frequently.

According to the second interpretation, system analysis is a specific method of cognition (the opposite of synthesis).

The third interpretation considers systems analysis as any analysis of any systems (sometimes it is added that analysis is based on systems methodology) without any additional restrictions on the scope of its application and the methods used.

According to the fourth interpretation, system analysis is a very specific theoretical and applied area of ​​research, based on systems methodology and characterized by certain principles, methods and scope. It includes both methods of analysis and methods of synthesis, which we briefly described earlier.

So, system analysis is a set of certain scientific methods and practical methods for solving various problems arising in all spheres of purposeful activity of society, based on systematic approach and representation of the research object in the form of a system. A characteristic feature of system analysis is that the search for the best solution to a problem begins with identifying and organizing the goals of the system during the operation of which the problem arose. At the same time, a correspondence is established between these goals, possible ways to solve the problem that has arisen and the resources required for this.

The purpose of system analysis is a complete and comprehensive verification of various options for action in terms of quantitative and qualitative comparison of the resources expended with the resulting effect.

System analysis is intended to solve primarily weakly structured problems, i.e. problems, the composition of elements and relationships of which are only partially established, problems that arise, as a rule, in situations characterized by the presence of an uncertainty factor and containing unformalizable elements that cannot be translated into the language of mathematics.

System analysis helps the person responsible for the decision to more strictly approach the assessment of possible options for action and choose the best one, taking into account additional, non-formalized factors and aspects that may be unknown to the specialists preparing the decision.

2. Causes of SA. Features of a perfect SA

Systems analysis arose in the United States and primarily in the depths of the military-industrial complex. In addition, in the United States, systems analysis has been studied in many government organizations. It was considered the most valuable spin-off in the field of defense and space exploration. In both houses of the US Congress in the 60s. last century, bills were introduced “on the mobilization and use of the country’s scientific and technical forces for the application of systems analysis and systems engineering in order to make the most complete use of human resources to solve national problems.”

System analysis was also used by managers and engineers in large industrial enterprises. The purpose of applying systems analysis methods in industry and in the commercial field is to find ways to obtain high profits.

An example of the use of systems analysis methods in the United States is the program planning system known as “planning-programming-budgeting” (PPB), or “program finance” for short.

In addition to the use of the PPB system, a number of forecasting and planning systems are used in the United States, which are based on systems analysis methods. In particular, the PATTERN information system was used to forecast and plan R&D; the FAIM automated information system was used to manage the Apollo space project at all stages of its development; with the help of the QUEST system, a quantitative relationship was achieved between military tasks and goals and the scientific and technical means necessary for their implementation, for the same purposes in industry, was the SKOR system.

The main methodological feature of these systems was the principle of sequential division of each problem into several tasks of a lower level in order to construct a “tree of goals.”

The systems under consideration made it possible to determine the time frame for solving scientific and technical problems and the mutual usefulness of the work, contributed to improving the quality of decisions made by overcoming a narrow departmental approach to their adoption, rejecting intuitive and strong-willed decisions, as well as work that cannot be completed within the established time frame.

At the same time, management practice in the United States in recent decades shows that the term “systems analysis” is not used as often as it was previously. Many approaches to justifying complex decisions that were associated with it continued to be used and developed quite intensively under new names - “program analysis”, “policy analysis”, “consequence analysis”, etc. At the same time, the “novelty” of these types of analysis lies rather in their names. Their methodological and methodological basis continues to be system analysis, the ideology of the systems approach.

Systems analysis is a scientific, comprehensive approach to decision making. The whole problem is studied as a whole, the development goals of the management object and various ways of their implementation are determined in the light of possible consequences. In this case, there is a need to coordinate the work of various parts of the control object, individual performers, in order to direct them to achieve a common goal.

No science is born overnight, but appears as a result of the coincidence of growing interest in a certain class of problems and the level of development of scientific principles, methods and means with the help of which it is possible to solve these problems. Systems analysis is no exception. Its historical roots are as deep as the roots of civilization. Even primitive man, when choosing a place to build a home, subconsciously thought systematically. But how scientific discipline system analysis took shape during the Second World War, first in relation to military tasks, and after the war - to the tasks of various spheres of civil activity, where it became effective means solving a wide range of practical problems.

It was at this time that the general foundations of systems analysis matured so much that they began to be formalized as an independent branch of knowledge. It can be said with good reason that the development of methods of systems analysis has greatly contributed to the fact that management in all spheres of human activity has risen from the stage of craft or pure art, which largely depended on the ability of individuals and their accumulated experience, to the stage of science.

3. The emergence and development of systemic ideas. Signs of systemicity

In our time, there is an unprecedented progress of knowledge, which, on the one hand, has led to the discovery and accumulation of many new facts and information from various areas of life, and thereby confronted humanity with the need to systematize them, to find the general in the particular, the constant in the changing. On the other hand, the growth of knowledge creates difficulties in its development and reveals the ineffectiveness of a number of methods used in science and practice. In addition, penetration into the depths of the Universe and the subatomic world, which is qualitatively different from the world commensurate with already established concepts and ideas, raised doubts in the minds of some scientists about the universal fundamentality of the laws of existence and development of matter. Finally, the process of cognition itself, which is increasingly taking the form of transformative activity, sharpens the question of the role of man as a subject in the development of nature, about the essence of the interaction between man and nature, and in connection with this, about the development of a new understanding of the laws of development of nature and their action. The fact is that transformative human activity changes the conditions for the development of natural systems, and thereby contributes to the emergence of new laws and trends of movement. In a number of studies in the field of methodology, a special place is occupied by the systems approach and, in general, by the “systems movement”. The systems movement itself was differentiated and divided into various directions: general systems theory, systems approach, systems analysis, philosophical understanding of the systemic nature of the world. There are a number of aspects within the methodology of systems research: ontological (is the world in which we live systemic in its essence?); ontological-gnoseological (is our knowledge systematic and is its systematicity adequate to the systematicity of the world?); epistemological (is the process of cognition systematic and are there limits system cognition peace?); practical (is human transformative activity systematic?)

The term system is understood as an object that is simultaneously considered both as a single whole and as a set of interconnected heterogeneous elements working as a single whole, united in the interests of achieving set goals. The systems differ significantly from each other both in composition and in their main goals. This whole acquires some property that is absent in the individual elements.

Signs of systematicity are described by three principles.

Signs of systemicity:

· External integrity - isolation or relative isolation of the system in the surrounding world;

· Internal integrity - the properties of a system depend on the properties of its elements and the relationships between them. Violation of these relationships can lead to the system being unable to perform its functions;

· Hierarchy - a system can be distinguished into various subsystems, on the other hand, the system itself is also a subsystem of another larger subsystem;

4. System ideas and practice. Ways to increase labor productivity

We will try to show that consistency is a universal property of matter and human practice. Let's start by considering human practical activity, i.e. its active and purposeful impact on nature. To do this, we will formulate only the most obvious and mandatory signs of systematicity: its integrity and structure, the interconnectedness of its constituent elements and the subordination of the organization of the entire system to a specific goal.

Another name for such a structure of activity is algorithmicity. The concept of an algorithm arose first in mathematics and meant specifying a precisely defined sequence of unambiguously understood operations on numbers or other mathematical objects.

Today it becomes obvious that the role of systemic ideas in practice is constantly increasing, that the very systematic nature of human practice is growing.

The last thesis can be illustrated with many examples; it is instructive to do this using a somewhat schematic example of the problem of increasing labor productivity.

Academician V. M. Glushkov showed that the complexity R of objectively necessary management tasks grows faster than the square of m people engaged in management activities: R >

5. The difference between the possibilities of solving the problem of labor productivity in complex systems and the previous stages. How the use of human intelligence is proposed

One of the most important features of social production is the continuous growth of its efficiency, and above all, the increase in labor productivity. Ensuring the growth of labor productivity is a very complex and multifaceted process, but its result is expressed and embodied in the development of means of labor and methods of its organization.

Academician V. M. Glushkov showed that the complexity R of objectively necessary management tasks grows faster than the square of m people engaged in management activities: R > b m?, where b = Const. It is known that for successful management of an industry where n people are employed and there are m managed objects, the total complexity of management tasks is determined by the relation R = c (n + m)? (usually c = 1). The objective trend of increasing management complexity, which takes place in modern world, also occurs in Russia (where n = 2731, m = 107). This leads to an increase in the necessary costs of living labor, i.e. resources R for management, and the capabilities of the human brain to remember and process information are limited. On average, a person's memory capacity is S = 10 16 bits, and the average computing performance is V = 1/3 106 operations/s.

Consequently, when solving complex information problems only by administrative bodies at the municipal and federal levels, we get R = 1 (2731 + 10000000)? = 10002731? = 100054627458000 operations/year, and for satisfactory management of the country with manual technology, at least N = R/V = 3x100054627458000/1000000 = 3001636882 people are required, i.e. 300 million. This is more than 2 times the country's population. To eliminate the shortage of living labor in governing the country, it is necessary to significantly increase (by N/m = 300 times) the work efficiency of each employee of the country’s governing apparatus. This was not required due to the automation of the information and analytical work of the country's governing bodies using computers.

Here it is very important to understand what to automate, i.e. be completely entrusted to the machine, only those works can be studied in detail, described in detail and fully, in which it is known exactly what, in what order and how to do it in each case, and all possible cases and circumstances in which it may turn out to be known exactly. machine. Only under such conditions can an appropriate machine be constructed, and only under these conditions can it successfully perform the work for which it is intended.

So, automation is a powerful tool for increasing productivity.

Thus, the solution to the problem of labor productivity in complex systems is achieved through automation. The role of human intelligence in this case is to develop automated devices.

6. Cognition processes and systematicity

It is known that a person masters the world in various ways. First of all, he masters it sensually, i.e. directly perceiving it through the senses. The nature of such cognition, which consists in memory and is determined by the emotional state of the subject, appears to us both holistically and fractionally - presenting the picture as a whole or fractionally, highlighting any moments. Based on emotional states, a person develops an idea of ​​the world around him. But sensory perception is also a property of all animals, not just humans. The specificity of man is a higher level of cognition - rational cognition, which allows one to detect and consolidate in memory the laws of motion of matter.

Rational cognition is systemic. It consists of successive mental operations and forms a mental system that is more or less adequate to the system of objective reality. Human practical activity is also systematic, and the level of systematic practice increases with the growth of knowledge and accumulation of experience. The systematicity of various types of reflection and transformation of reality by man is ultimately a manifestation of the universal systematicity of matter and its properties.

Systemic cognition and transformation of the world presupposes: consideration of the object of activity (theoretical and practical) as a system, i.e. as a limited set of interacting elements, determining the composition, structure and organization of elements and parts of the system, identifying the main connections between them, identifying the external connections of the system, identifying the main ones, determining the function of the system and its role among other systems, analyzing the dialectics of the structure and function of the system, detection on this basis of patterns and trends in the development of the system.

Knowledge of the world, and “scientific knowledge” in particular, cannot be carried out chaotically, disorderly; it has a certain system and is subject to certain laws. These laws of cognition are determined by the laws of development and functioning of the objective world.

7. Development of system views

Considering the historical stages of development of systemic concepts, it is important to trace the unity and struggle of two opposing approaches to knowledge, analytical and synthetic. In the early stages of human development, the synthetic approach prevailed. F. Engels noted that in ancient Greece undivided knowledge prevailed: nature is considered in general, as one whole. The universal connection of natural phenomena is not proven in detail: it is the result of direct contemplation.

The subsequent stage of the metaphysical way of thinking is characterized by the predominance of analysis: The decomposition of nature into its individual parts, the division of various processes and objects of nature into certain classes, the study of the internal structure of organic bodies according to their anatomical forms - all this was the main condition for the gigantic successes that were achieved in the field knowledge of nature over the past four hundred years.

A new, higher level of systematic cognition is a dialectical way of thinking. Representatives of German classical philosophy made a significant contribution to the development of dialectics: I. Kant, I. Fichte, F. Schelling. Kant most accurately expressed judgments about systematicity: The unity achieved by reason is the unity of the system

The idealistic understanding of the system found its peak in Hegel. And only liberation from idealism led to the modern understanding of systematicity. Much of the philosophical understanding of the system was developed by Marx and Lenin.

M.A. was the first to explicitly raise the question of a scientific approach to managing complex systems such as society. Ampere. When constructing a classification of all kinds of sciences (Experience in the Philosophy of Sciences, or an analytical presentation of the classification of all human knowledge Part 1 1834, Part 2 1843), he identified a special science of government and called it cybernetics. At the same time, he emphasized its systemic features: “The government constantly has to choose from various measures the one that is most suitable for achieving the goal, and only through an in-depth and comparative study of the various elements provided to it for this choice (...) can it formulate general behavior rules.

The next stage of development is associated with the name A.A. Bogdanova (real name Malinovsky). The first volume of his book General Organizational Science (Tektology) was published in 1911, and in 1925 the third volume. Bogdanov's idea was that all objects and processes have a certain level of organization. Tectology should study the general patterns of organizations at all levels. He notes that the higher the level of organization, the more the properties of the whole differ from the simple sum of the properties of its parts.

In fact, the study of systems theory began under the influence of the need to build complex technical systems primarily for military purposes. Sufficient funds have been allocated and significant results have been achieved.

The next stage in the development of systemic concepts is associated with the name of the Austrian biologist L. Bertalanffy. He tried to create a general theory of systems of any nature based on the structural similarity of the laws of various disciplines.

The current state of systems theory is associated with the research of the famous Belgian scientist Ilya Romanovich Prigogine, winner of the 1977 Nobel Prize. While studying the thermodynamics of nonequilibrium physical systems, he realized that the patterns he discovered applied to systems of any nature. Its main results are related to the self-organization of systems. At turning points or bifurcation points, it is fundamentally impossible to predict whether the system will become more or less organized.

8. Models and simulation

Modeling is one of the main methods of cognition, is a form of reflection of reality and consists in finding out or reproducing certain properties of real objects, objects and phenomena with the help of other objects, processes, phenomena, or using an abstract description in the form of an image, plan, map , a set of equations, algorithms and programs.

The possibilities of modeling, that is, transferring the results obtained during the construction and research of the model to the original, are based on the fact that the model in a certain sense displays (reproduces, models, describes, imitates) some features of the object that are of interest to the researcher.

Replacing one object (process or phenomenon) with another, but preserving all the essential properties of the original object (process or phenomenon), is called modeling, and the replacing object itself is called a model of the original object

The following classes of models can be distinguished.

Material models

The common feature shared by these models is that they copy the original object. They are usually made from a completely different, often cheaper, material than the original object. The sizes of models can also differ greatly from the original object in one direction or another.

Information models

A model that represents an object, process or phenomenon with a set of parameters and connections between them is called an information model. Revealing the connections between the parameters of an information model is often perhaps the most difficult part in building a model, occurring after its parameters have been determined. Information models of the same object, intended for different purposes, can be completely different. For example, an information model of a person can be presented in the form of a verbal portrait, photograph, information entered in a medical card or the file of the personnel department at the place of work. The class of information models is wide. These include verbal (verbal) models, databases, diagrams and diagrams, drawings and drawings, mathematical models, etc. An information model in which the parameters and dependencies between them are expressed in mathematical form is called a mathematical model.

For example, the well-known equation S=vt, where S is distance, and v and t are speed and time, respectively, is a model of uniform motion expressed in mathematical form. (Give other examples of mathematical models)

The rapid development of computer technology contributes to the rapid development and improvement of information modeling tools and methods; solving problems based on information models (computer modeling) is one of the most important areas of application of modern computers. The subject of computer modeling can be: the economic activity of a company or bank, industrial enterprise, information and computer network, technological process, any real object or process, for example, the inflation process, and in general - any Complex System.

It is safe to say that most of the models that a person uses to solve life problems represent a certain set of elements and connections between them. Such models are usually called systems, and general methods building system models - a systems approach. The foundations of the systems approach were laid down in his works by L. von Bertalanffy. In systems, the elements that make it up cannot be considered in isolation. Their total contribution to the functioning of the system as a whole is determined by the interaction of the elements with each other.

9. Modeling - components of purposeful activity

One of the problems that is almost always encountered when conducting systems analysis is the problem of experimenting in or on a system. Very rarely this is permitted by moral or security laws, but is often associated with material costs and (or) significant losses of information.

The experience of all human activity teaches that in such situations it is necessary to experiment not on an object, a subject or system that interests us, but on their models. This term does not necessarily mean a physical model, i.e. a copy of an object in a reduced or enlarged form. Physical modeling is very rarely applicable in systems that are in any way connected with people. In particular, in social systems (including economic ones) one has to resort to mathematical modeling.

One more important circumstance must be taken into account during mathematical modeling. The desire for simple, elementary models and the resulting ignorance of a number of factors can make the model inadequate to the real object, or, roughly speaking, make it untruthful. Again, system analysis cannot be done without active interaction with technologists, specialists in the field of laws of functioning of systems of this type.

In economic systems, one has to resort mostly to mathematical modeling, albeit in a specific form - using not only quantitative, but also qualitative, as well as logical indicators.

Models that have worked well in practice include: intersectoral balance; growth; economic planning; prognostic; balance and a number of others.

Concluding the question of modeling when performing system analysis, it is reasonable to raise the question of the correspondence of the models used to reality.

This correspondence or adequacy may be obvious or even experimentally verified for individual elements of the system. But already for subsystems, and even more so for the system as a whole, there is the possibility of a serious methodological error associated with the objective impossibility of assessing the adequacy of the model of a large system at the logical level.

In other words, in real systems, logical justification of element models is quite possible. These models strive to be built as minimally sufficient, as simple as possible without losing the essence of the processes. But humans are no longer able to logically comprehend the interaction of tens or hundreds of elements. And it is here that the corollary from the famous Gödel theorem, known in mathematics, can “work” - in a complex system completely isolated from outside world, there may be truths, positions, conclusions that are completely “acceptable” from the standpoint of the system itself, but have no meaning outside of this system.

That is, it is possible to build a logically flawless model of a real system using element models and analyze such a model. The conclusions of this analysis will be valid for each element, but a system is not a simple sum of elements, and its properties are not just a sum of the properties of elements.

This leads to the conclusion that without taking into account the external environment, conclusions about the behavior of the system obtained on the basis of modeling can be quite justified when viewed from within the system. But it is also possible that these conclusions have nothing to do with the system when viewed from the outside world.

10. Methods of implementing the model. Abstract material models

When a person creates models, he has two types of means at his disposal: the means of consciousness itself and the means of the surrounding material world; Accordingly, models are divided into abstract (ideal) and material (real).

Abstract models.

These include language constructs, i.e. language models. Natural language is a universal means of constructing any abstract models. Universality is ensured by the possibility of introducing new words into the language, as well as the possibility of hierarchical construction of increasingly developed language models. The universality of language is achieved, among other things, by the fact that language models have ambiguity, precision, and vagueness. This manifests itself already at the level of words (ambiguity or uncertainty). Plus the versatility of combining words into phrases. This gives rise to approximateness - an inherent property of language models.

Material models.

In order for some material object to be a model, a replacement for some original, a relationship of similarity must be established between them. There are different ways to do this:

1). Direct likeness obtained as a result of physical interaction in the process of creating a model (photography, scale models of airplanes, ships, buildings, dolls, templates, patterns, etc.). Even for a direct similarity to the model, there is a problem of transferring the simulation results to the original (the result of hydrodynamic tests of the ship model, in which the speed of movement can be scaled according to the characteristics of water (viscosity, density, gravity - cannot be scaled)). There is a theory of similarity that relates to direct similarity models.

2). Indirect similarity is established between the original and the model not as a result of physical interaction, but exists objectively in nature, revealed in the form of a coincidence or proximity of their abstract models. For example, the electromechanical analogy. Some patterns of mechanical and electrical processes are described by the same controls, the only difference is in the different physical interpretation of the variables included in these controls. Therefore, experimenting with a mechanical design can be replaced by experimenting with an electrical circuit, which is simpler and more effective. Doctors' experimental animals are analogues of the human body, an autopilot is an analogue of a pilot, etc.

3) Conditional similarity. The similarity of the model to the original is established as a result of agreement. Examples: an identity card is a model of its owner, a map is a model of terrain, money is a model of value, signals are models of messages. Models of conditional similarity are a way of material embodiment of abstract models, a form in which these abstract models are stored and transmitted from one person to another, while maintaining the possibility of returning to an abstract form. This is achieved by agreement on what state of a real object is associated with a given element of the abstract model.

The specification and deepening of the general scheme of conditional similarity models occurs in two directions: - conditional similarity models in technical devices, where they are used without human intervention; signals - the rules of construction and methods of using signals are called code, encoding, decoding - are studied special disciplines; models of conditional similarity created by man himself - sign systems. The field of knowledge dealing with this is called semiotics.

11. Establishing the similarity of material models

Similarity is a certain relationship between the values ​​of indicators of the properties of various objects, observed and measured by the researcher in the process of cognition. Similarity is understood as such a one-to-one correspondence (relationship) between the properties of objects in which there is a function or rule for bringing the values ​​of indicators of these properties of one object to the values ​​of the same indicators of another object.

Mathematical (formal) descriptions of such objects allow their reduction to an identical form.

In other words, similarity is the relationship of one-to-one correspondence between the values ​​of indicators of homogeneous properties of different objects. Properties that have the same dimension of indicators are called homogeneous.

Several types of object similarity are known.

1. Depending on the completeness of taking into account the parameters, the following are distinguished:

· absolute (theoretical) similarity, which assumes proportional correspondence of the values ​​of all parameters of these objects, i.e.

pj(t) / rj(t) = mj(t), where j=1,n;

· practical similarity - a certain functional one-to-one correspondence of parameters and indicators of a certain subset of properties that are essential for this study;

· practical complete similarity - correspondence of indicators and parameters of the selected properties in time and space;

· practically incomplete similarity - correspondence of parameters and selected properties of indicators only in time, or only in space;

practical approximate similarity - compliance of the selected parameters and indicators with certain assumptions and approximations.

2. According to the adequacy of the nature of objects, they are distinguished:

· physical similarity, which presupposes the adequacy of the physical nature of objects (special cases of physical similarity are mechanical, electrical and chemical similarity of objects);

· mathematical similarity, which assumes the adequacy of the formal description of the properties of objects (special cases of mathematical similarity are statistical, algorithmic, structural and graphic similarity of indicators of the properties of objects).

The problem of identifying similar objects is the selection of scientifically based similarity criteria and the development of methods for calculating these criteria.

12. Conditions for implementing model properties

According to the logic of system analysis, when an interrelated set of tasks for project implementation has been identified and built (one can say, and this would be quite strict, a system of tasks), the next stage of system design begins - the study of the conditions for implementing the model.

Naturally, any system model can be implemented in practice only if certain conditions are present.

Let's show it using the example of the education system.

Naturally, any model of the educational system can be implemented in practice only if certain conditions are present: personnel, motivational, material and technical, scientific and methodological, financial, organizational, legal, information.

To the credit of policymakers, it should be noted that last years Much more attention began to be paid to the issues of conditions for the implementation of educational reforms and their similarities, just as to the technological preparation for the implementation of educational projects: the creation of the necessary textbooks, methodological developments for the retraining of teachers, etc. In the old days, already six months after the release of the next resolution, it was necessary to report to the CPSU Central Committee that schools, vocational schools, etc. “switched to a new content of education.”

13. Model and original. Differences. Finiteness, simplicity, proximity

The correspondence between model and reality can be expressed by the following principles:

1. Limb.

All real objects, as part of the real world, are infinite in their properties and connections with other objects. However, if we keep in mind our cognitive capabilities, then here we are limited by our own resources - the number of nerve cells in the brain, the number of actions that we can perform per unit of time, the time itself during which we can solve some problem; the external resources that we can involve in the process of our activities are limited, i.e. it is necessary to cognize the infinite world with finite means. All models are finite. Abstract models are finite from the start - they are immediately endowed with a fixed number of properties. Real models are finite in the sense that from the infinite set of their properties, only a few are selected and used, similar to the properties of the original object that interest us. The model is similar to the original in a finite number of relations.

2. Simplification.

The finiteness of models makes their simplification inevitable, but in human practice this simplification is acceptable, because For any purpose, an incomplete, simplified reflection of reality is sufficient. For specific purposes, such simplification is also necessary, because allows you to identify the main effects and properties of the original (physical abstractions - ideal gas, absolute black body, ...).

Forced simplification of the model - the need to operate with it - resource simplification.

Another aspect: of two models that describe a certain object with equal accuracy, the one that is simpler turns out to be closer to the original (to its true nature).

3. Approximation of models.

This term is associated with the quantitative difference between the model and the original (qualitative differences are associated with the terms finitude and simplicity). This quantitative difference always exists and in itself is neither large nor small; its measure is introduced by correlating this difference with the purpose of modeling (a clock is a time model).

4. Adequacy.

The model with the help of which the set goal is successfully achieved is adequate. This is not equivalent to the concept of completeness, accuracy, or correct accuracy of the model. Ptolemy's model is adequate (in the sense of accurately describing the motion of the planets). An adequate but false model (successful healing using spirit spells). Sometimes it is possible to introduce some measure of adequacy. Then we can consider questions about identifying the model (i.e., finding the most adequate one in a given class), about the stability of models, about their adaptation.

14. Similarity between the model and the original. Adequacy of the model. The truth of models. Combination of truth and falsity

The most important concept in economic and mathematical modeling, as in any modeling, is the concept of model adequacy, i.e., the correspondence of the model to the modeled object or process. The adequacy of a model is to some extent a conditional concept, since there cannot be a complete correspondence of a model to a real object, which is also typical for economic and mathematical modeling. When modeling, we mean not just adequacy, but compliance with those properties that are considered essential for the study. Verifying the adequacy of economic and mathematical models is a very serious problem, especially since it is complicated by the difficulty of measuring economic quantities. However, without such verification, the use of modeling results in management decisions may not only be of little use, but also cause significant harm.

Bearing in mind precisely the theoretical considerations and methods underlying the construction of the model, one can raise questions about how accurately this model reflects the object and how completely it reflects it. (In the modeling process, special stages are distinguished - the stage of model verification and assessment of its adequacy). In this case, the thought arises about the comparability of any human-made object with similar natural objects and about the truth of this object. But this only makes sense if such items are created with special purpose depict, copy, reproduce certain features of a natural object.

Thus, we can say that truth is inherent in material models: - due to their connection with certain knowledge; - due to the presence (or absence) of isomorphism of its structure with the structure of the modeled process or phenomenon; due to the relationship of the model to the modeled object, which makes it part of cognitive process and allows you to solve certain cognitive problems.

And in this regard, the material model is epistemologically secondary and acts as an element of epistemological reflection.

15. Dynamics of the model. Modeling process. Reasons for the impossibility of complete algorithmization of the modeling process

At the input and output we have the dependences of the parameters X and Y on time t. The challenge is to define the black box.

Let us assume that a single signal X(t) is applied to the input of the system, which was previously in zero initial conditions. If an exponential signal is observed at the output, then this is a first order system. To describe it, one derivative is sufficient, and the solution to the model will contain one integral. Since one integral “always generates” one exponential, two integrals are two exponentials. To determine whether a curve is exponential, a tangent is drawn at each point until it intersects the steady-state line. At any point T must be a constant value. The value T characterizes the inertia of the system (memory). At a small value of T, the system weakly depends on the previous history and the input instantly causes the output to change. When T is large, the system responds slowly to the input signal, and when T is very large, the system remains unchanged.

The first order link has two parameters:

1) inertia - T

2) gain

Let us introduce the concept of a transfer function as a model of a dynamic system. By definition, the transfer function is the ratio of output to input

The transfer function of the first order link has the form.

Then, using the definition of the transfer function, we have where "p" is the symbol for the derivative ().

Next we get:

In difference form, the equation can be written as (Yi+1 - Yi)*T+Yi*dt = k*Xi*dt. Or expressing the present through the past Yi+1 = A* Xi + B* Yi. Here A and B are weighting coefficients. A indicates the weight of component X, which determines the influence of the external world on the system, B indicates the weight of Y, which determines the memory of the system, the influence of history on its behavior.

In particular, if B=0, then Yi+1 = A* Xi and we are dealing with an inertia-free system that instantly responds to the input signal Y=k*X and increases it by k times. If B = 0.5, then it is easy to obtain that with a constant input signal X, Yi+1 = A* Xi +0.5* Yi = A* Xi +0.5(A* Xi-1 +B* Yi-1) = ... = A*(1+0.5+0.52+...+0.5n)*Хi-n+0.5n+1*Yi-n = 2*A*Xi-n = k*Xi-n or, depicted on a graph, we get a damping exponential. Y tends to the value of the input signal X multiplied by the gain k.

If we further strengthen the influence of the past B=1, then the system will begin to integrate itself (the output is fed to the system input)

Yi+1 = A* Xi + Yi adding the input signal all the time, which corresponds to exponential unlimited growth of the output signal. In essence, this corresponds to positive feedback. When B=-1, we have the model Yi+1 = A* Xi - Yi in meaning corresponding to negative feedback. When defining a model, it is necessary to find the unknown coefficients k and T.

Let's consider the second-order link.

The second order link has three parameters.

Characteristics: smooth exit from zero, inflection point and endless progress towards a steady state.

A model is a material or mentally imagined object that replaces the original object in the process of study and preserves its typical features that are significant for a given study. The process of building a model is called modeling.

The modeling process consists of three stages - formalization (transition from a real object to a model), modeling (research and transformation of the model), interpretation (translation of modeling results into reality).

16. Model model. First definition of the model. Second definition of the model

Model - an object or description of an object, a system for replacing (under certain conditions, proposals, hypotheses) one system (i.e., the original) with another system for studying the original or reproducing any of its properties. A model is the result of mapping one structure onto another.

Models, if we ignore the areas and spheres of their application, are of three types: cognitive, pragmatic and instrumental.

A cognitive model is a form of organization and presentation of knowledge, a means of connecting new and old knowledge. A cognitive model, as a rule, is adjusted to reality and is a theoretical model.

A pragmatic model is a means of organizing practical actions, a working representation of the goals of the system for its management. Reality in them is adjusted to some pragmatic model. These are usually applied models.

An instrumental model is a means of constructing, researching and/or using pragmatic and/or cognitive models.

Cognitive ones reflect existing ones, and pragmatic ones - although not existing ones, but desirable and, possibly, feasible relationships and connections.

According to the level, “depth” of modeling, models are empirical - based on empirical facts, dependencies, theoretical - based on mathematical descriptions, and mixed, semi-empirical - using empirical dependencies and mathematical descriptions.

The mathematical model M describing the system S (x1,x2,...,xn; R) has the form: M=(z1,z2,...,zm; Q), where ziIZ, i=1,2,.. .,n, Q, R - sets of relations over X - the set of input, output signals and states of the system and Z - the set of descriptions, representations of elements and subsets of X, respectively.

Basic requirements for the model: clarity of construction; visibility of its basic properties and relationships; its availability for research or reproduction; ease of research, reproduction; preservation of information contained in the original (with the accuracy of the hypotheses considered when constructing the model) and obtaining new information.

The modeling problem consists of three tasks: building a model (this task is less formalizable and constructive, in the sense that there is no algorithm for building models); model research (this task is more formalizable; there are methods for studying various classes of models); use of the model (constructive and specific task).

Model M is called static if there is no time parameter t among xi. A static model at each moment of time provides only a “photograph” of the system, its slice.

The model is dynamic if among xi there is a time parameter, i.e. it displays the system (processes in the system) over time.

A model is discrete if it describes the behavior of the system only at discrete moments in time.

A model is continuous if it describes the behavior of the system for all points in time from a certain period of time.

A model is a simulation if it is intended for testing or studying, reproducing possible paths of development and behavior of an object by varying some or all parameters xi of the M model.

A model is deterministic if each input set of parameters corresponds to a completely definite and uniquely defined set of output parameters; otherwise, the model is non-deterministic, stochastic (probabilistic).

We can talk about different modes of using models - a simulation mode, a stochastic mode, etc.

The model includes: object O, subject (optional) A, task Z, resources B, modeling environment C: M=.

The properties of any model are:

finiteness: the model reflects the original only in a finite number of its relations and, in addition, modeling resources are finite; simplicity: the model displays only the essential aspects of the object; approximate: reality is represented by the model roughly or approximately; adequacy: the model successfully describes the system being modeled; information content: the model must contain sufficient information about the system - within the framework of the hypotheses adopted when constructing the model.

Life cycle of the simulated system:

· Collecting information about the object, putting forward hypotheses, pre-model analysis;

· Designing the structure and composition of models (submodels);

· Construction of model specifications, development and debugging of individual submodels, assembly of the model as a whole, identification (if necessary) of model parameters;

· Model research - selection of research method and development of a modeling algorithm (program);

· Study of the adequacy, stability, sensitivity of the model;

· Evaluation of modeling tools (expended resources);

· Interpretation, analysis of modeling results and establishment of some cause and effect relationships in the system under study;

· Generation of reports and design (national economic) solutions;

· Refinement, modification of the model if necessary, and return to the system under study with new knowledge obtained through modeling.

17. Multiplicity of system models. Definition of the concept of “problem”, “goal”, “system”

One of the fundamental principles of modeling complex systems is the principle of multiplicity of models, which consists, on the one hand, in the possibility of representing many different systems and processes using the same model and, on the other hand, in the possibility of representing the same system by many different models. depending on the purposes of the study. Using this principle makes it possible to abandon the approach whereby a separate model is developed for each system under study, and to propose new approach, in which abstract mathematical models of different levels (mainly basic and local) are developed, used to study systems of various classes. In this case, the modeling task comes down to competent parameterization of models and interpretation of the results obtained.

The goal is a complex combination of various conflicting interests. The goal is a system-forming, integrating factor that unites individual objects and processes into integrity, into a system. This unification occurs on the basis that isolated objects cannot always serve as sufficient means to achieve human goals. And in their combined form they acquire a new, systemic, integral quality, which is sufficient to achieve goals.

The system is a means to achieve a goal.

The first definition of the system is complemented by the second, which characterizes its internal structure.

The general definition of a system is formulated as follows: “A system is a set of interacting elements isolated from the environment for a specific purpose.”

A problem is a situation characterized by a difference between the required (desired) output and the existing output. An exit is necessary if its absence poses a threat to the existence or development of the system. The existing output is provided by the existing system. The desired output is provided by the desired system. The problem is the difference between the existing and desired system. The problem may be preventing output from decreasing or increasing output. The problem condition represents the existing system (“known”). The requirement represents the desired system.

18. "Black box". Model, properties, difficulties in building a model. Conditions for the usefulness of the black box model

Building a black box model can be challenging task due to the multiplicity of inputs and outputs of the system (this is due to the fact that any real system interacts with environment unlimited number of ways). When building a model, a finite number must be selected from them. The selection criterion is the purpose of the model, the significance of a particular connection in relation to this goal. Here, of course, errors are possible; those connections not included in the model (which are still valid) may turn out to be important. This is of particular importance when determining the goal, i.e. system outputs. A real system interacts with all objects of the environment, so it is important to take into account all the most essential things. As a result, the main goal is accompanied by the setting of additional goals.

Example: a car must not only carry a certain number of passengers or have the required load capacity, but also not create too much noise when driving, have exhaust gas toxicity that does not exceed the norm, acceptable fuel consumption, ... Fulfilling only one goal is not enough, failure to meet additional goals can make it even harmful to achieve the main goal.

The black box model sometimes turns out to be the only applicable one when studying systems.

Example: a study of the human psyche or the effect of a drug on the body, we act only on the inputs and draw conclusions based on observations of the outputs in the time signal for the user, because Each watch shows the state of its sensor, then their readings gradually diverge. The solution is to synchronize all clocks according to the readings of a certain time standard ("precise time" signals via radio). Should the standard be included in the clock as a system or should each clock be considered as a subsystem in the overall time indicating system?

19. Model of system properties. Element, subsystems, reasons for constructing different models by different experts

A system is a collection of interconnected elements, isolated from the environment and interacting with it as a single whole.

The property that arises from the combination of parts is the main feature, essence, essence of the phenomenon. The concept of a phenomenon is, first of all, an idea of ​​the essence of the phenomenon, of the main feature of the phenomenon, of the property generated in a given system.

For example, televisions and cars are different: small and large, good and not so good, assembled according to different schemes from different parts. But they all have some distinctive properties: a television is a phenomenon that receives television signals and reproduces a television image, and a car is a “cart that drives itself.”

To form a concept about a phenomenon means: to indicate the existence of a phenomenon - to highlight the phenomenon, to distinguish it; show the structure of the phenomenon; prove the relationship of this phenomenon with others, i.e. determine the place of this phenomenon in the hierarchy of phenomena.

The hierarchy and nesting of phenomena arises from the fact that in phenomena-supersystems the properties of phenomena-subsystems generated by their integrity are involved. Every property of a phenomenon is generated at some level of the hierarchy of phenomena, therefore, when studying phenomena, it is necessary to distinguish between properties inherited from the constituent parts and properties generated by the integrity of the phenomenon.

Since each property, each entity is generated at its own level of the hierarchy of phenomena, there is no point in looking for properties at lower levels - they are not there yet. It is also pointless to study properties at higher levels - there properties can be absorbed and included in other phenomena-systems.

In addition to linear, hierarchical ordering, there are other types of it. However, despite this, in order to master any property of a phenomenon, it is necessary to understand the structure of that level of hierarchy at which the properties of the phenomena of interest are generated. This is the essence of a systematic approach to the analysis of phenomena.

The complexity of the phenomena occurring at each level of the hierarchy is limited. Any phenomenon generated at this level of the hierarchy is based on a combination of some of the 7 principles. These are the principles of the methodology of cognition.

A quantitative characteristic of a functional property is called a functional PARAMETER.

For example, the component parts of the phenomenon influence each other along a circuit of connections: in a car, the fuel system supplies the engine with a combustible mixture, and the engine creates a rotating force on the shaft.

The engine is the subsystem of the car that generates the rotating force. The set of engine parts is the carrier of the phenomenon that generates rotational force, and the interaction between the parts is the circuit of connections of the engine parts.

Since the phenomena are independent of their carriers, all parts in an engine can be replaced, and in a car one engine can be replaced with another, which also generates a rotating force on the shaft.

So, the internal structure of a phenomenon, the architecture of a system, is a set of functional properties of its constituent parts and the structure of connections between them.

20. System structure model. Terms of use, definition of “system structure”, “relationship”, “property”. The relationship between the concepts of “relationship” and “properties”. Second definition of the system

The black box model and composition are not enough in many cases. It is necessary to know the connections between elements and subsystems, or relationships. The set of necessary or sufficient relationships between elements to achieve a goal is called the structure of the system. There is a huge (maybe infinite) number of connections between real objects included in the system. When defining a structure model, only a finite number of connections are considered that are significant in relation to the goal in question.

Example: when calculating a mechanism, the force of mutual attraction of the parts to each other is not taken into account, but the weight of the parts is necessarily taken into account.

When we are talking about a connection or relationship, at least two objects are involved. A property is an attribute of one object. But the property is revealed in the process of interaction of the object with other objects, i.e. when establishing some relationship.

Example: the ball is red, but this is detected in the presence of a white source and a light analyzer receiver. A property is a collapsed relation. Hypothesis: This statement is true for all properties.

The second definition of a system: “A system is a set of interconnected elements, isolated from the environment and interacting with it as a whole.”

21. Block diagram of the white box system. Graphs

The second definition of a system: “A system is a set of interconnected elements, isolated from the environment and interacting with it as a whole.” This definition covers black box, composition, and structure models. It is called a system block diagram (white box).

Example: block diagram of a clock.

Abstraction from the content side of structural diagrams leads to a diagram in which only the presence of elements and connections between them is indicated. In mathematics, such an object is called a graph. (graph - diagram, graph, graph). In a graph, there are vertices (the elements correspond to them) and edges (the connections correspond to them). If the connections are not symmetrical, then they are denoted by edges with arrows (arc) and the graph is called oriented, otherwise it is called undirected. You can reflect differences between elements and connections by assigning numerical characteristics to edges (edge ​​weight - weighted graph) or by revealing vertices and edges (colored graph). There are two types of system dynamics:

- functioning - processes occurring in a system that stably realizes a fixed goal (clock, public transport, cinema, TV, ...);

- development - changing the system when its goals change. The existing structure of the system must change (and sometimes its composition) to support the new purpose.

Dynamic models can also be constructed in the form of a black box, a composition model (a list of steps in a sequence of actions), or a block diagram model (for example, in the form of a network diagram when describing some production process). Formalization of the concept dynamic system is carried out by considering the correspondence between the set of possible values ​​of inputs X, outputs Y and an ordered set of moments of time T

T->X; T->Y; Tеt, Tеx, x=x(t), y=y(t).

The black box model is a combination of two processes (x(t)), (y(t)). Even if we assume that y(t)=F(x(t)), then in the black box model the transformation F is unknown.

22. Dynamic models of the system. Operation and development

The object model represents the static structure of the designed system (subsystem). However, knowledge of the static structure is not enough to understand and evaluate the operation of the subsystem.

It is necessary to have means for describing the changes that occur with objects and their connections during the operation of the subsystem. One such tool is a dynamic subsystem model. It is built after the object model of the subsystem has been built and previously agreed upon and debugged. The dynamic model of a subsystem consists of state diagrams of its objects and subsystems.

Dynamic models are used to evaluate developmental phenomena.

A dynamic model of a system consists of state diagrams of its objects and subsystems.

The current state of an object is characterized by a set of current values ​​of its attributes and relationships. During operation of the system, its constituent objects interact with each other, as a result of which their states change. The unit of influence is an event: each event leads to a change in the state of one or more objects in the system, or to the occurrence of new events. The operation of a system is characterized by the sequence of events occurring in it.

The functioning (and development) of the system is possible if the system includes:

1. "Elements" - subsystems;

2. A single “Managing structure” - a system-forming factor;

3. Possibility of exchange with the environment (within and within the system) of matter, energy, and information.

The functioning of the formed system occurs at two levels:

1. Management uses fictions;

2. An element (a subsystem represented as a “whole”) is a phantom and uses “data”.

A given is something that exists without our assistance as a fact.

Fact (from Latin factum - done, accomplished) - 1) event; actual - valid.

2) done, accomplished; the reality in front of us, that which is recognized as really existing.

Thus, experiencing Events-Facts, the Element changes.

The control structure receives a signal that the element has changed.

Thus we have:

The element is

Event-Fact change Signal

The control structure is

Signal receiving a signal determining the characteristics of the signal determining the significance of the signal Concept

In fact, here we are seeing a transition

Event-Fact Signal Concept

Thus

The control structure is one reality (Concepts), and the Element (a subsystem presented as a “whole”) is another reality (Event-Fact).

But the Transition between realities is made only by a SIGNAL (from the Latin signum - sign), a sign that carries a message (information) about an event, the state of an object under observation, or transmits control commands, alerts, etc.

Thus, the Functional system is:

- Element incoming Signal Event-Fact outgoing Signal - Control structure incoming Signal Concept outgoing Signal

But since the “Element” is, in turn, also a “System”, the picture of the Functional system is more complicated:

The Control Structure generates an outgoing Signal based on the Concept, and the Element (subsystem) generates an outgoing Signal based on the Event-Fact.

Therefore, for the system to function properly, it needs

- A signal that correctly reflects the Event-Fact;

- The mechanism of correct formation of the Concept.

23. Transformation of a formal model into a meaningful one. Recommendations for achieving model completeness

With all the unimaginable diversity of real systems, there are very few fundamentally different types of system models: a “black box” model, a composition model, a relationship model, as well as their reasonable combinations and, above all, the unification of all three models, i.e. system structure. This applies both to static models that reflect the fixed state of the system and to dynamic models that reflect the nature of temporary processes that occur with the system. We can say that the structure ("white box") is obtained as a result of the "summation" of the "black box" models, composition and relations. All of these types of models are formal, relevant to any system and, therefore, not related to any specific system. To obtain a model of a given system, it is necessary to give the formal model specific content, i.e. decide which aspects of a real system to include as elements of a model of the chosen type, and which not, considering them unimportant. This process is usually informal, since signs of materiality or insignificance in very rare cases can be formalized (such cases include, for example, the possibility of taking as a sign of materiality the frequency of occurrence of a given element in various similar, i.e., equally classified, systems). Equally poorly formalized are the signs of elementaryness and the signs of differentiation between subsystems.

For these reasons, the process of constructing meaningful models is a creative process. Nevertheless, the intuition of an expert developing a content model is greatly helped by the formal model and recommendations for filling it with specific content. The formal model is a “window” through which the expert looks at the real system, building a meaningful model.

In the process of constructing meaningful models of systems, the need to use dialectics is clearly visible. In this process, the main task is to create a complete model. General recommendations for achieving completeness follow from the basic principles of dialectics:

- it is necessary to strive to take into account all significant factors influencing the phenomenon under consideration; since such materiality is not always obvious, it is better to include an unimportant element in the model than not to include an essential one;

- one of the necessary signs of the completeness of a model is the presence of contradictory elements in it; special attention should be paid to this point: for example, when listing outputs, it is necessary to include in the list not only desirable target outputs (connections, products, etc.), but also undesirable ones (waste, defects, etc.);

No matter how extensive our knowledge about a given phenomenon is, reality is richer than models - there are always unknown factors in it; In order not to lose sight of the possibility of something significant, but still unknown, it is recommended to include implicit “spare”, non-specific elements in the model (such as “everything else”, “something else”) and refer to these elements at various stages of system analysis , as if posing the question: is it time to supplement the model with another explicit element? These recommendations, of course, do not exhaust all possibilities: the arsenal of the art of modeling includes many scientifically based methods and empirical heuristics.