Process approach to IT management. Reference models. The reference model of the teacher's competence The ideal reference model in which the main

room

Name

Level 1

Process in progress

AP 1.1

Process execution attribute

Level 2

Guided process

AP 2.1

Execution control attribute

AP 2.2

Work Product Control Attribute

Level 3

Established process

AP 3.1

Process definition and transformation attribute

AP 3.2

Process resource attribute

Level 4

Predictable process

AP 4.1

Process Dimension Attribute

AP 4.2

Process control attribute

Level 5

Optimizing process

AP 5.1

Process change (verification) attribute

AP 5.2

Improvement Opportunity Attribute

Scale

Process attributes

Assessment

Level 1

Process execution

Mainly or completely

Level 2

Process execution

Execution control

Work product management

Completely

Mainly or completely

Mainly or completely

Level 3

Process execution

Execution control

Work product management

Process resource

Completely

Completely

Completely

Mainly or completely

Mainly or completely

Level 4

Process execution

Execution control

Work product management

Process definition and transformation

Process resource

Process measurement

Process control

Completely

Completely

Completely

Completely

Completely

Mainly or completely

Mainly or completely

Level 5

Process execution

Execution control

Work product management

Process definition and transformation

Process resource

Process measurement

Process control

Process change

Possibility of further improvement

Completely

Completely

Completely

Completely

Completely

Completely

Completely

Mainly or completely

Mainly or completely

Process

room

Name

room

Name

Acquisition (basic)

Purchase preparation (component)

Supplier selection (component)

Supplier Verification (Component)

Customer approval (component)

Support (basic)

Establish Requirements (New)

Functioning (advanced)

Functional use (extended component)

User support (advanced component)

Development (basic)

Analysis and development of system requirements (component)

Analysis of software requirements (component)

Software development (component)

Software design (component)

Software integration (component)

Software testing (component)

System testing and integration (component)

System and software operation (basic)

Supporting life cycle processes

Documenting (advanced)

Configuration management (basic)

Quality assurance (basic)

Verification (basic)

Validation (basic)

Joint review (baseline)

Check (basic)

Problem solving (basic)

Measurement (new)

Reusable (new)

Management (basic)

Project management (component)

Quality management (new)

Risk management (new)

Organizational alignment (new)

Improvement process (basic)

Process creation (component)

Process Assessment (Component)

Process improvement (component)

Human Resource Management (advanced)

Infrastructure (basic)

Table 4.4.

Activities and processes 12207

Processes 15504

Initial life cycle processes

Acquisition process

Acquisition process

basic

Initialization

Acquisition preparation process

Component

Preparation of the Application-for-Offer [-application for the contract]

Supplier selection process

Component

Contract preparation and adjustment

Supplier selection process

Component

Supplier verification

Supplier verification process

component

Acceptance and completion

Customer approval process

component

Delivery process

Delivery process

basic

Initialization

Delivery process

basic

Preparing a response

Delivery process

basic

Contract

Delivery process

basic

Planning

Delivery process

basic

Execution and management

Delivery process

basic

Review and evaluation

Delivery process

basic

Delivery and completion

Delivery process

basic

Requirements establishment process

Development process

Development process

basic

Process implementation

Development process

basic

Analysis of system requirements

component

System architecture development

System requirements development and analysis process

component

Analysis of software requirements

Software Requirements Analysis Process

component

Software architecture development

Software development process

component

Working software design

Software development process

component

Software coding and testing

Software design process

component

Software integration

Software integration process

component

Software qualification testing

Software testing process

component

System integration

component

System qualification testing

System testing and integration process

component

Software installation

Delivery process

basic

Program support

Delivery process

basic

Functioning process

basic

Process implementation

Functional use process

extended component

Functional testing

Functional use process

extended component

System operation

Functional use process

extended component

User support

User support process

extended component

Operation process

basic

Process implementation

Software and system operation process

basic

Analysis of problems and modifications

Software and system operation process

basic

Modification implementation

Software and system operation process

basic

Commissioning

Software and system operation process

basic

Migration

Software and system operation process

basic

Utilization of software

Software and system operation process

basic

Supporting life cycle processes

Documentation process

Documentation process

extended

Process implementation

Documentation process

extended

Development and development

Documentation process

extended

Products

Documentation process

extended

Exploitation

Documentation process

extended

Configuration management process

Basic

Process implementation

Configuration management process

basic

Configuration identification

Configuration management process

basic

Configuration control

Configuration management process

basic

Configuration status accounting

Configuration management process

basic

Configuration assessment

Configuration management process

basic

Release and delivery management

Configuration management process

basic

Quality assurance process

Quality assurance process

basic

Process implementation

Quality assurance process

basic

Product warranty

Quality assurance process

basic

Process guarantee

Quality assurance process

basic

Quality assurance systems

Quality assurance process

basic

Verification process

Verification process

basic

Process implementation

Verification process

basic

Verification

Verification process

basic

Validation process

basic

Process implementation

Validation process

basic

Plausibility check

Validation process

basic

Joint review process

Joint review process

basic

Process implementation

Joint review process

basic

Project Management Reviews

Joint review process

basic

Technical reviews

Joint review process

basic

Verification process

Verification process

basic

Process implementation

Verification process

basic

Verification process

basic

Problem solving process

Problem solving process

basic

Process implementation

Problem solving process

basic

Solution of problems

Problem solving process

basic

Measurement process

Reuse process

Organizational Life Cycle Processes

Management process

Management process

basic

Initialization and scoping

Project management process

component

Planning

Project management process

component

Execution and control

Project management process

component

Review and evaluation

Project management process

component

Closing

Project management process

component

Quality management process

Risk management process

Organizational alignment process

Infrastructure process

Infrastructure process

basic

Process implementation

Infrastructure process

basic

Infrastructure creation

Infrastructure process

basic

Infrastructure Operation

Infrastructure process

basic

Improvement process

Improvement process

basic

Process creation

Process creation process

component

Process evaluation

Process Assessment Process

component

Process improvement

Improvement process

component

Process preparation

extended

Process implementation

Human Resource Management Process

extended

Preparation of essential development

Human Resource Management Process

extended

Preparing the implementation of the plan

Human Resource Management Process

Methodological materials on organizational, methodological, psychological and pedagogical support for professional growth, self-realization of teachers and the formation of key competencies, a profile of competencies of a teacher were developed by the regional scientific and methodological center for expert assessment of pedagogical activities of the State Budgetary Educational Institution of Higher Professional Education of the Moscow Region "Academy of Social Management"

The text is provided for your reference.
The reference model of the competence of a pedagogical worker, developed in the regional scientific and methodological center for expert assessment of pedagogical activity, due to its characteristics, is a normative, predictive model aimed at the result, therefore it underlies the control and measuring materials used in certification, defining their goals, objectives and content ...

We present a reference model of the competence of a teacher in a graphical and descriptive form.

Picture 1- Reference model of key competencies of a teacher

The reference model of the teacher's competence (Figure 1) is an ideal, verbalized, that is, encoded with signs of a natural language, a teacher's model, which is an ideal image, a standard of a specialist that meets all the requirements for teaching staff during certification for the first and highest qualification categories, pp. 30, 31 of the Procedure for attestation of pedagogical workers of state and municipal educational institutions, the requirements set forth in the unified qualification reference book of positions of managers, specialists and employees (annex to the order of the Ministry of Health and Social Development of the Russian Federation of August 26, 2010 No. 761 n), and professional standards.

When designing a reference model of a teacher's competence, we relied on the author's developments, various scientific schools, in particular, we used the domestic research of I.A. Winter, N.V. Kuzmina, A.K. Markova, and foreign studies of the Council of Europe.

Key competence we consider it as an integral characteristic of a pedagogical worker, which allows him to freely navigate in the social and professional space, to perform professional activities efficiently and effectively, to solve standard and non-standard professional and pedagogical tasks, to be a socially adapted person, capable of constant personal and professional self-development.

The scope of competence is competency profiles as components of its knowledge, skills and attitudes, meaningfully determining competence.

Figure 2 - Special and professional competence

Special and professional competence (Figure 2), that is, possession of their own professional activities at a sufficiently high level, the ability to project their further professional development.

understanding the purpose, mission of the profession;

possession of the norms of professional activity, high efficiency;

achieving high results and their stability; professional excellence;

professional consciousness (awareness of the maximum number of signs of professional activity: content, means, labor results);

professional thinking, professional intuition, independence in solving professional problems;

optimal psychological cost of the result, no fatigue and overload.

Within the special and professional competence highlights the following competency profiles :

1. Subject competence , that is, the depth, consistency of knowledge on the subject and their application in teaching practice; the ability to implement curricula of basic and elective courses in various educational institutions.

2. Organizational and methodological competence , i.e. readiness to apply modern educational methods and technologies, including informational ones, to ensure the quality of the educational process; activities, actions, techniques, skills, methods of work, techniques used in this profession to successfully achieve a result; ability to organize educational activities of students (pupils).

3. Diagnostic competence , i.e. possession of psychological and pedagogical knowledge, psychological and pedagogical actions, methods, techniques, skills, techniques, technologies; the ability to apply modern methods of diagnosing the achievements of students and pupils; carry out pedagogical support of the processes of socialization and professional self-determination of students, preparing them for a conscious choice of profession.

4. Analytical and evaluative competence , that is, the ability to analyze and evaluate the formation of universal educational actions, mental operations of students, taking into account their individual characteristics and capabilities, both in qualitative and quantitative indicators (points in the rating, category, etc.); apply methods of mathematical and statistical processing of information; participate in professional tests, the result of which is a differentiated (qualitative and quantitative) assessment of professionalism.

5. Predictive competence , that is, the ability to determine growth prospects, zones of proximal development of their students and their professional development; to be aware of the potential opportunities of schoolchildren and their own; awareness of development prospects and opportunities for their implementation (prognostic criteria); self-design, self-experimentation; building your own strategy for professional growth, building and implementing a scenario for your professional life; consistency between the motivational and operational side of the activity.

6. Research competence , that is, the ability to apply the methods of theoretical and experimental research; plan, organize, conduct and analyze a pedagogical experiment on the implementation of innovations; ability to analyze and synthesize; research skills; the ability to generate new ideas (creativity); demonstrate an understanding of the quality of research relevant to the discipline; Demonstrate an understanding of experimental verification of scientific theories.

Figure 3 -

Communicative competence (Figure 3) - competence of social interaction as the ability to adequately establish mutual understanding, avoid conflicts, create a climate of trust; referring oneself to a professional community; possession of the norms of professional communication, ethical norms of the profession; orientation of professional results for the benefit of other people, their spiritual enrichment with the means of their profession; the ability to cooperate, make contacts, easy compatibility; competitiveness, the ability to arouse interest in society in the results of their professional activities.

Communicative competence manifests itself in the followingcompetency profiles :

1. Social and communicative competence , that is, the ability to find verbal and non-verbal means and ways of forming and formulating a thought during its generation and perception, adequate to situations of interaction; the ability to use public speaking skills, including in the field of broadcasting their own experience (the ability to broadcast their own positive experience to the pedagogical community: articles, speeches, participation in competitions; ability to conduct discussions, polemics; willingness to interact with colleagues).

2. Organizational and communicative competence , that is, the ability to organize productive communication and cooperation of schoolchildren; the ability to conduct educational activities in the form of dialogues, polemics, disputes, discussions, exchange of views, scientific disputes, etc.

Figure 4 - Information competence

Information competence (Figure 4) is related to information technology ownership:

• receiving, processing, issuing information; transformation of information (reading, note-taking);
• mass media, multimedia technologies, computer literacy;
• possession of electronic, Internet technology.

Information competence is manifested in the following profiles:

1. Information retrieval competence , that is, the ability to find the necessary information from various sources.

2. Information and analytical competence , that is, the skills to analyze information and manage it; readiness to use the basic methods, methods and means of obtaining, storing, processing information; willingness to work with a computer as a means of information management; ability to work with information in global computer networks.

3. Information technology competence , that is, the ability to use, reproduce, improve the means and methods of obtaining and reproducing information in printed and electronic form; knowledge of basic applied programs and the ability to use them; Computer skills.

Figure 5 - Personal competence

Personal competence, i.e., stable professional motivation, the presence of a positive self-concept, creative attitude, conscious professional creativity, changing oneself by means of the profession; individuality in professional work; openness to continuous professional training, experience accumulation, change; possession of the techniques of self-realization and development of individuality within the framework of the profession, readiness for professional growth, the ability for individual self-preservation; self-development of professional abilities; strong goal-setting; professional learning; reliance on past professional experience, continuity; an increase in individualization and relative autonomy with professional growth.

Profiles personal competence:

1. Self-development and self-expression competence - sustainable motivation, ability to set goals, professional abilities, professional learning ability, self-presentation, positive emotions; ability and readiness for education throughout life, possession of methods of personal self-expression and self-development, means of resisting professional deformations of the individual.

2. Reflexive competence - a system-forming component of professional pedagogical activity and the quality of a person, which allows reflection to be carried out most effectively and adequately, which ensures development and self-development, promotes a creative approach in educational and professional activities, achieving their maximum efficiency and effectiveness; acmeological phenomenon contributing to the achievement of the highest results in activities; professional and personal qualities of a teacher, his readiness and ability for reflective activity using knowledge, skills, skills, professional and life experience; ability for introspection and self-esteem.

The idea of \u200b\u200bcontrol according to the reference model, proposed in 1961, can be realized with a slight modification of the circuit in Fig. 11.27. This idea had a great influence on the work on control systems. Its essence is to build, synthesize or adapt a system, the overall impulse response of which best matches the characteristic of the reference model or the characteristic of some ideal model.

Suppose, for example, that the dynamic characteristics of aircraft control differ significantly for speeds up to the sound barrier and supersonic. To provide the pilot with the ability to adequately control the aircraft, regardless of its speed, an autopilot is introduced, which receives the pilot's control signals and actuates the control servos. The response of the aircraft to pilot control signals corresponds to the response of some reference model, which is chosen by the system designer to provide the aircraft with a “steering feel” that is convenient for pilots. Many physical systems are synthesized so that their characteristics are similar to those of models, and many of these systems are adaptive.

It is not difficult to implement the described approach by modifying the circuits in Fig. 11.11 or 11.27. To do this, simply replace the inverse delayed model with the reference model. The overall performance of the system is then more likely to be similar to that of the reference model than simply a delayed jump. Such a modification of the circuit is shown in Fig. 11.28.

In the systems in Fig. 11.11 and 11.27, the delay is introduced to allow accurate inverse modeling, corresponding to a low level of rms deviation. If there is a delay, you can get a delayed, but more accurate response. As noted above, the introduction of a delay is necessary in cases where there is a response delay in the controlled system or this system is not a minimum phase. When replacing the delay with the reference model, in cases where the delay is needed for accurate inverse modeling, it is usually necessary to introduce it into the reference model.

Figure: 11.28. Control with an adaptive inverse model, similar to Fig. 11.27, but with the inclusion of the reference model

In this case, it is necessary to form such a characteristic of the reference model, which can be realized by sequentially switching on the controlled system and the adaptive filter, if the weight coefficients of this filter correspond to the minimum standard deviation. The diagram in Fig. 11.28 works well when flexible conditions are specified for an adaptive system. However, one should not assume that this circuit is less inertial or has a more accurate response than is possible for the controlled system and its adaptive control device with a finite impulse response.

For an example of an adaptive control system using inverse modeling using a reference model, consider the following implementation of the circuit in Fig. 11.28:

reference model: the weights in the weights model in the adaptive process iteration control unit. In fig. 11.29 shows the response to a unit jump of an uncompensated controlled model, and Fig. 11.30 - the response of the compensated system, superimposed on the response of the reference system. Obviously, a very close approximation has been obtained.

Model classification

The problem of classifying models, like any fairly complex phenomena and processes, is complex and multifaceted. The objective reason for this is that the researcher is only interested in one property (or several properties) of the system (object, process, phenomenon), for which the model was created. Therefore, the classification can be based on many different classification features: description method, functional purpose, degree of detail, structural properties, scope, etc.

Let's consider some of the most frequently used classes (types) of models (Table 1.4.1).

Table 1.4.1

Material(physical, real) models - models built by means of the material world to reflect its objects, processes.

Ideal(imaginary) models - models built by means of thinking on the basis of our consciousness.

Information(abstract, theoretical) models - models built on one of the languages \u200b\u200b(sign systems) for coding information.

Material Modelsare real, material constructions that serve to replace the original in a certain respect. The main requirement for the construction of this class of models is the requirement of similarity (similarity, analogy) between the model and the original. There are several types of similarity - geometric, physical, analogy, etc.

Geometric similarityis the basic requirement for the construction of geometric models, which are an object geometrically similar to its prototype and serving for demonstration purposes. Two geometrical figures are similar if the ratio of all respective lengths and angles is the same. If you know the coefficient of similarity - the scale, then simply multiplying the size of one figure by the scale value determines the size of the other figure. In the general case, such a model demonstrates the principle of operation, the relative position of parts, the process of assembly and disassembly, the layout of the object and is intended to study properties that are invariant (independent) from the absolute values \u200b\u200bof the linear dimensions of the object. Examples of geometric models are: car models, mannequins, sculptures, prostheses, globes, etc. They depict the prototype not in all the variety of its properties, not in any qualitative boundaries, but in purely spatial boundaries. Here there is a similarity (similarity) not generally between things, but between special types of things - bodies. This is the limitation of this class of models. Note that direct similarity is realized here.

Physical similarityrefers to the model and the original of the same physical nature and reflects their similarity in the same ratios of the same physical variables in the corresponding space-time points. Two phenomena are physically similar if, according to the given characteristics of one, the characteristics of the other can be obtained by simple recalculation, which is analogous to the transition from one system of units of measurement to another. Geometric similarity is a special case of physical similarity. With physical similarity, the model and the original can be in more complex geometric relationships than linear proportionality, since the physical properties of the original are not proportional to its geometric dimensions. It is important here that the physical variable space of the model is similar to the physical variable space of the original. In this case, the physical model in relation to the original is an analogy of the type of isomorphism (one-to-one correspondence). The central problem is the problem of correct recalculation of the results of a model experiment for the results of testing the original in real conditions. The similarity is based on meeting some physical criteria.

Ideal(imaginary) models are ideal constructions in our minds in the form of images or ideas about certain physical phenomena, processes, objects, systems (geometric point, infinity, etc.).

Abstract(theoretical, informational) models - models representing objects of modeling in figurative or symbolic form.

Examples of abstract models are some hypothesis 1 about the properties of matter, assumptions about the behavior of a complex system under conditions of uncertainty, or a new theory about the structure of complex systems.

On abstract models and on speculative analogy (similarity) between the model Mand original Sabstract (theoretical) modeling is being built.

A prominent representative of abstract and symbolic modeling is the mathematical model.

Mathematical model– it is a set of mathematical formulas, equations, relations, describing the properties of the object of modeling of interest to the researcher.

To investigate each aspect of modeling (type, structure, behavior) or their combination, appropriate models can be used: appearance models, structure models, behavior patterns.

Appearance modelmost often comes down to listing the external features of the object of modeling and is intended for identification (recognition) of the object.

Structure modelis a list of the constituent elements of the modeling object with an indication of the links between these elements and is intended for visual display, study of properties, identification of significant connections, study of the stability of the object of modeling

Behavior modelis a description of changes in the appearance and structure of a modeling object over time and as a result of interaction with other objects. The purpose of the behavior models is to predict the future states of the modeling object, manage objects, establish connections with other objects external to the modeling object.

Objectively, the levels of our perceptions, the levels of our knowledge about various phenomena, processes, systems are different. This is reflected in the ways of representing the phenomena under consideration.

TO informal models can be attributed to displays (images) obtained using various forms of thinking: emotions, intuition, figurative thinking, subconsciousness, heuristics as a set of logical techniques and rules for finding the truth. In unformalized modeling, the model is not formulated, but instead some fuzzy mental reflection (image) of reality is used, which serves as the basis for decision-making.

An example of vague (intuitive) ideas about an object is a fuzzy description of a situation based on experience and intuition.

TO formalized models include figurative models, when the models are built from any visual elements (elastic balls, fluid flows, trajectories of bodies, etc.).

Formalizable abstract models include sign models, including mathematical constructions, programming languages, natural languages, together with the rules for their transformation and interpretation.

By their purpose, the models are designed to solve many problems:

research(descriptor, cognitive, conceptual, formal) models are designed to generate knowledge by studying the properties of an object;

educationalmodels are designed to transfer knowledge about the studied object;

workers(optimization, management) models are designed to generate the right actions in the process of achieving the goal.

TO research models include semi-natural stands, physical models, mathematical models. Note that research models can act as training models if they are designed to transfer knowledge about the properties of an object. Examples of working models are: a robot; autopilot; a mathematical model of an object built into a control or monitoring system; artificial heart, etc. At the same time, research and teaching models should be close to reality, and working models should reflect this reality. There is no clear line between these models. So, for example, a research model that adequately reflects the properties of an object can be used as a working one.

Research models are carriers of new knowledge, teaching models combine old knowledge with new.

Working models idealize accumulated knowledge in the form of ideal actions to perform certain functions that would be desirable to perform.

Descriptor models- descriptive models are designed to establish the laws of change in the parameters of these processes and are implementations of descriptive and explanatory meaningful models at the formal level of modeling.

As an example of such a model, we can cite the model of the motion of a material point under the action of applied forces, using Newton's second law. By specifying the position and speed of the point at the initial moment of time (input values), the point mass (model parameter) and the law of variation of the applied forces (external influences), it is possible to determine the speed and coordinates of the point at any subsequent moment in time (output values).

Cognitive(mental, cognitive) model - models that represent a kind of mental image of an object, its ideal model in the head of a researcher, obtained as a result of observing the original object.

Forming such a model, the researcher, as a rule, seeks to answer specific questions, therefore, everything unnecessary is cut off from the infinitely complex structure of the object in order to obtain its more compact and laconic description.

Cognitive models are subjective, as they are formed speculatively based on all previous knowledge and experience of the researcher. One can get an idea of \u200b\u200bthe cognitive model only by describing it in a sign form. The representation of a cognitive model in natural language is called meaningful model .

Cognitive and content models are not equivalent, since the former may contain elements that the researcher cannot or does not want to formulate.

Conceptual modelit is customary to call a meaningful model, in the formulation of which the concepts and representations of subject areas of knowledge are used that study the object of modeling.

In a broader sense, a conceptual model is understood as a meaningful model based on a certain concept or point of view.

Formal modelis a representation of a conceptual model using one or more formal languages \u200b\u200b(for example, mathematical theory languages, universal modeling language, or algorithmic languages).

In the humanities, the modeling process in many cases ends with the creation of a conceptual model of the object.

In natural science and engineering disciplines, as a rule, it is possible to build a formal model.

Thus, cognitive, content and formal models make up three interrelated levels of modeling.

Optimization models- models designed to determine the optimal (best) parameters of the simulated object from the point of view of a certain criterion, or to find the optimal (best) control mode for a certain process.

As a rule, such models are built using one or more descriptive models and include some criterion that allows you to compare different options for sets of values \u200b\u200bof output quantities with each other in order to choose the best one. Restrictions in the form of equalities and inequalities related to the features of the object or process under consideration can be imposed on the range of values \u200b\u200bof the input parameters.

An example of an optimization model is modeling the process of launching a rocket from the Earth's surface in order to lift it to a given height in minimaltime under restrictions on the magnitude of the impulse of the engine, the time of its operation, the initial and final mass of the rocket. In this case, the mathematical relations of the descriptive model of the rocket motion appear in the form of constraints such as equalities.

Note that for most real processes, structures, it is required to determine the optimal parameters at once according to several criteria, i.e. we are dealing with the so-called multicriteria optimization problems.

Management models- models used to make effective management decisions in various areas of purposeful human activity.

In general, decision-making is a process comparable in complexity to the process of thinking in general. However, in practice, decision-making is usually understood as the choice of some alternatives from a given set of them, and the general decision-making process is represented as a sequence of such choices of alternatives.

Unlike optimization models, where the selection criterion is considered definite and the desired solution is established from the conditions of its extremality, in management models it is necessary to introduce specific optimality criteria that allow comparing alternatives with various uncertainties of the problem. The type of the optimality criterion is not fixed in advance in management models. This is the main feature of these models.

Registration modelsare models designed to register properties and qualities of interest to the researcher that are not available for direct registration at the modeling object.

When solving problems of managing complex dynamic objects, reference and prognostic models are used, which are a formalized display of the desired characteristics of a controlled object for the purposes of current or future object management.

Reference modelIs a model that describes in one form or another the desired (idealized) properties of the object of modeling (control).

Predictive models- models designed to determine futurestates ( the futurebehavior) of the modeling object.

Simulation modelsIs a set of descriptions of system elements, interrelationships of elements with each other, external influences, algorithms for the functioning of the system (or rules for changing states) under the influence of external and internal disturbances.

Simulation models are created and used when the creation of a unified model of a complex system is impossible or involves very great difficulties, the available mathematical methods do not allow obtaining satisfactory analytical or numerical solutions of the problems under consideration. But the presence of descriptions of elements and algorithms of functioning makes it possible to simulate the process of functioning of the system and produce measurementscharacteristics of interest.

It can also be noted that simulation models can be created for a much wider class of objects and processes than analytical and numerical models. In addition, since for implementation, as a rule, computing means (computers and other means) are used, universal or special algorithmic languages \u200b\u200bserve as means of formalized description of simulation models.

Simulation modeling when studying large (complex) systems

remains practically the only available method of obtaining information about the behavior of a system under conditions of uncertainty, which is especially important at the stage of its design. Using this method, one can select the structure, parameters and control algorithms of the synthesized system, evaluate their efficiency, and also simulate the behavior of the system under conditions that cannot be reproduced on a real prototype (for example, accidents, failures, emergencies, etc.). When the behavior of the system under the action of random factors is studied in imitation modeling with subsequent statistical processing of information, then it is advisable to use the method of static modeling as a method of machine implementation of the simulation model. At the same time, the method of statistical tests (Monte Carlo method) is considered as a numerical method for solving analytical problems.

A special class of models are cyberneticmodels that reflect the management aspects of the behavior of complex systems based on information exchange between its elements. The very physical nature of cybernetic models differs from the physical nature of the prototype and its elements. A feature of cybernetic models is the possible presence in them, in addition to the control mechanism, also mechanisms of self-organization, learning, adaptation, etc., and in more complex systems - and artificial intelligence.

Taking into account the time factor in modeling leads to the use of static and dynamic models.

Static modelsreflect the steady-state (equilibrium) operating modes of the system;

Static modes of operation of elements, objects, systems are reflected in their static characteristics (linear, nonlinear) and are described by the corresponding algebraic functional dependencies.

Dynamic modelsreflect unsteady (nonequilibrium, transient) modes of system operation.

Differential equations or systems of differential equations are most often used to describe non-equilibrium (transient) modes of system operation.

Let us consider some of the properties of models that allow, to one degree or another, either to distinguish or to identify a model with an original (object, process). It is customary to distinguish the following properties of models: adequacy, complexity, finiteness, truth, proximity.

Adequacy.Under adequacyit is customary for models to understand the correct qualitative and quantitative description of an object (process) for a selected set of characteristics with some reasonable degree of accuracy.

Adequacy is the most important requirement for a model; it requires the model to correspond to its real object (process, system, etc.) with respect to the selected set of its properties and characteristics. In this case, we mean the adequacy not in general, but the adequacy for those properties of the model that are essential for the researcher. Full adequacy means the identity between the model and the prototype.

A mathematical model can be adequate with respect to one class of situations (state of the system + state of the external environment) and not adequate with respect to another. The use of an inadequate model can lead either to a significant distortion of the real process or properties (characteristics) of the studied object, or to the study of nonexistent phenomena, properties and characteristics.

You can introduce the concept of the degree of adequacy, which will vary from 0 (lack of adequacy) to 1 (complete adequacy). The degree of adequacy characterizes the proportion of the truth of the model relative to the selected characteristic (property) of the object under study. Note that in some simple situations, the numerical assessment of the degree of adequacy is not particularly difficult. The difficulty in assessing the degree of adequacy in the general case arises from the ambiguity and vagueness of the criteria of adequacy themselves, as well as because of the difficulty of choosing those signs, properties and characteristics by which the adequacy is assessed.

The concept of adequacy is a rational concept, therefore, increasing its degree should also be carried out at a rational level. The adequacy of the model should be checked, monitored, refined constantly in the process of research on particular examples, analogies, experiments, etc. As a result of the adequacy check, it is found out what the assumptions made lead to: either to an acceptable loss of accuracy, or to a loss of quality. When checking the adequacy, it is also possible to justify the legality of the application of the accepted working hypotheses in solving the problem or problem under consideration.

Simplicity and complexity.The simultaneous demand for simplicity and adequacy of the model is controversial. From the point of view of adequacy, complex models are preferable to simple ones. In complex models, a greater number of factors can be taken into account that affect the studied characteristics of objects. Although complex models more accurately reflect the simulated properties of the original, they are more cumbersome, difficult to visualize and inconvenient to use. Therefore, the researcher seeks to simplify the model, since it is easier to operate with simple models. When striving to build a simple model, the basic model simplification principle:

you can simplify the model as long as the basic properties, characteristics and patterns inherent in the original are preserved.

This principle indicates the limit of simplification.

Moreover, the concept of simplicity (or complexity) of a model is a relative concept. A model is considered simple enough if modern research tools (mathematical, informational, physical) make it possible to carry out qualitative and quantitative analysis with the required accuracy. And since the capabilities of research tools are constantly growing, those tasks that were previously considered difficult can now be classified as simple.

A more difficult task is to ensure the simplicity / complexity of the model of a complex system, consisting of separate subsystems connected to each other in some hierarchical and multi-connected structure. Moreover, each subsystem and each level have their own local criteria of complexity and adequacy, different from the global criteria of the system.

In order to reduce the loss of adequacy, it is more expedient to simplify models:

1) at the physical level while maintaining the basic physical relationships,

2) at the structural level while maintaining the basic systemic properties.

Simplification of the models at the mathematical level can lead to a significant loss of the degree of adequacy. For example, truncation of a high-order characteristic equation to the 2nd - 3rd order can lead to completely incorrect conclusions about the dynamic properties of the system.

Note that simpler models are used to solve the synthesis problem, and more complex exact models are used to solve the analysis problem.

Finite models.It is known that the world is infinite, like any object, not only in space and time, but also in its structure (structure), properties, relations with other objects. Infinity manifests itself in the hierarchical structure of systems of various physical nature. However, when studying an object, the researcher is limited to a finite number of its properties, connections, resources used, etc. He, as it were, “cuts out” from the infinite world some finite fragment in the form of a specific object, system, process, etc. and tries to know the infinite world through the finite model of this fragment.

The finiteness of systems models lies, first, in the fact that they reflect the original in a finite number of relations, i.e. with a finite number of connections with other objects, with a finite structure and a finite number of properties at a given level of study, research, description, available resources. Secondly, the fact that the resources (information, financial, energy, time, technical, etc.) of modeling and our knowledge as intellectual resources are finite, and therefore objectively limit the possibilities of modeling and the very process of cognizing the world through models. Therefore, the researcher (with rare exceptions) deals with finite-dimensional models.

The choice of the model dimension (its degrees of freedom, state variables) is closely related to the class of problems to be solved. The increase in the dimension of the model is associated with problems of complexity and adequacy. In this case, it is necessary to know what is the functional relationship between the degree of complexity and the dimension of the model. If this dependence is power-law, then the problem can be solved by using computer systems. If this dependence is exponential, then the “curse of dimension” (R. Kalman 1) is inevitable and it is practically impossible to get rid of it.

As noted above, an increase in the dimension of the model leads to an increase in the degree of adequacy and, at the same time, to a complication of the model. Moreover, the degree of complexity is limited by the ability to operate with the model, i.e. by those modeling tools available to the researcher. The need to move from a rough simple model to a more accurate one is realized by increasing the dimension of the model by invoking new variables that are qualitatively different from the main ones and which were neglected when building a rough model. These variables can be classified into one of the following three classes:

1) fast flowingvariables, the extent of which in time or space is so small that, when roughly considered, they were taken into account by their integral or averaged characteristics;

2) slow flowingvariables, the extent of change of which is so great that in rough models they were considered constant;

3) small variables(small parameters), the values \u200b\u200band effects of which on the main characteristics of the system are so small that they were ignored in rough models.

Note that the division of the complex motion of the system in terms of speed into fast and slow motion makes it possible to study them in a rough approximation independently of each other, which simplifies the solution of the original problem. As for small variables, they are usually neglected when solving the synthesis problem, but they try to take into account their influence on the properties of the system when solving the analysis problem.

When modeling, one strives, if possible, to single out a small number of main factors, the influence of which is of the same order and is not too difficult to describe mathematically, and the influence of other factors can be taken into account using averaged, integral or "frozen" characteristics.

Approximation of models.It follows from the above that the finiteness and simplicity (simplification) of the model characterize qualitythe difference (at a structural level) between the original and the model. Then the approximation of the model will characterize quantitativeside of this difference.

You can introduce a quantitative measure of approximation by comparing, for example, a rough model with a more accurate reference (full, ideal) model or with a real model. Model closeness to the original inevitable, exists objectively, since the model as another object reflects only certain properties of the original. Therefore, the degree of approximation (proximity, accuracy) of the model to the original is determined by the statement of the problem, the purpose of modeling.

Excessive striving for increased model accuracy leads to its significant complication, and, consequently, to a decrease in its practical value. Therefore, apparently, the principle of L. Zadeh is true 1 that when modeling complex (human-machine, organizational) systems, accuracy and practical meaning are incompatible and exclude each other. The reason for the inconsistency and incompatibility of the requirements for the accuracy and practicality of the model lies in the uncertainty and vagueness of knowledge about the original itself - its behavior, its properties and characteristics, about the behavior of the environment, about the mechanisms of goal formation, ways and means of achieving it, etc.

The truth of the models.There is some truth in each model, i.e. any model in some way correctly reflects the original. The degree of truth of the model is revealed only when it is practically compared with the original, because only

practice is the criterion of truth.

On the one hand, any model contains the unconditionally true, i.e. definitely known and correct. On the other hand, the model also contains the conditionally true, i.e. true only under certain conditions. A typical mistake in modeling is that researchers apply certain models without checking the conditions for their truth, the limits of their applicability. This approach will lead to incorrect results.

Note that any model also contains the supposedly true (plausible), i.e. something that can be either true or false under uncertainty. Only in practice is the actual relationship between true and false in specific conditions established. Thus, when analyzing the truth level of the model, it is necessary to find out:

1) accurate, reliable knowledge;

2) knowledge that is reliable under certain conditions;

3) knowledge assessed with a certain degree of uncertainty;

4) knowledge that cannot be estimated even with a certain degree of uncertainty;

5) ignorance, i.e. what is unknown.

Thus, the assessment of the truth of the model as a form of knowledge is reduced to identifying the content in it of both objective reliable knowledge that correctly reflects the original, and knowledge that roughly estimates the original, as well as what constitutes ignorance.

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