Evolutionary models., Elements of the theory of modeling. - Modeling of systems

Evolutionary models.

The impossibility of confining itself to only one universal model is due to the fact that, on the one hand, different goals are set before these models, and on the other hand, they describe the processes occurring at times

personal time scales, and the degree of completeness of the model, its correspondence to the real object depends on the purposes for which this model is used. Models of the first type are mainly epistemological in character, they require a close connection with the methods of that particular area of ​​knowledge for which they are built. Models of this type are sufficiently inertial in their development, because they reflect the evolution in a particular area of ​​knowledge. Such models will be called evolutionary. Models of the second type are informative in nature and must correspond to specific goals for making decisions on the management of the object, which they describe. Such models will be called desensized. The division into epistemological (evolutionary) and informational (desicienated) models is relatively arbitrary, but it is convenient for reflecting modeling purposes.

In the information models used directly for decision-making in CS, the requirement of promptness is one of the main. It is caused by the fact that, at every impact on the OS, it is necessary to take into account in the model the actual changes that occurred in the object, and external disturbances, on the basis of which the control is calculated. This requirement of efficiency, that is, the need for the operation of such a model in the RMW, often leads to the abandonment of complex and accurate models, to the development of special, so-called robust, model building algorithms, the use of which usually leads to the stated goal in CS [18, 21] , 43, 54].

The appearance of identification in the early 60's was due to the urgent need to develop methods for constructing information models of OS. The absence of such models constrained the process of automation of these objects, the use of computers in the control loop. The objects turned out to be unprepared for the introduction of computer technology due to the lack of their mathematical description, their information models. The construction of an information model by identification methods should be aimed at eliminating this gap and developing methods for the operational receipt of the OS model. In this case, the identification methods should provide for the use of computers for solving the problems of building an information model.

Elements of the theory of modeling.

The absence of formal methods of transition from epistemological models to informational ones in modern management theory does not provide an opportunity to obtain from the available information an adequate description necessary for the creation of SS. But taking into account the information contained in epistemological models can significantly increase the amount of a priori information about the OS under consideration. Having set the goal of constructing an epistemological model of the process of functioning of system 5 for obtaining the necessary a priori information for constructing an effective SS and narrowing the class of modeling objects to a concrete one, i.e., before the behavior of a concrete system, 5 we solve the problem of constructing an applied theory of evolutionary and desensitized modeling that allows efficient realizing aspect) to move from epistemological ("research") models to informational ("management") models. It is most simple to make such a transition if both these classes of models are based on a single conceptual model, use a unified information system (knowledge base) and have a single criterial system. Let us first consider the features of epistemological and informational models.

The question of the applicability of some mathematical model to studying a given object is not a purely mathematical question and can not be solved by mathematical methods. Only the criterion of practice makes it possible to compare various hypothetical models and choose from them one that is the simplest and at the same time correctly conveys the properties of the object under study, that is, the system S.

Focusing on general questions of the methodology of modeling complex technical systems, we formulate the requirements for the applied theory of modeling, or more precisely - the elements of this theory in its application for solving a specific task. As noted above, this problem is posed as follows. It is necessary to first build and implement on the computer an evolutionary model of the process of functioning of system 5, obtained in the course of strategic identification of the OS, and then on its basis to construct a design model used to solve practical problems of operational control in an adaptive SS network. Or, using the terminology of the theory of identification, it is necessary to construct a specific discrete adaptive control system with an identifier and a predictor (combined) in the feedback loop (DASK), i.e., first implement a strategic identifier, and then on its basis a tactical operational identifier and a predictor, as OU is not the real system 5 (in view of its absence), but the machine model of the process of its functioning.

Thus, it is possible to treat the task posed as the task of automating the investigation of an object (the computer model M m ) for the synthesis of the tactical and operational model used directly in system management loop 5, and then to test the overall management performance.

Before proceeding to the presentation of the elements of the theory of process modeling in system 5, we give a number of definitions. Recall that by modeling we mean the study of an object by studying its model, that is, of another object more convenient for this purpose. Under the complexity of the modeled object, we will actually understand the complexity of the information about it (its description), depending on the purposes of modeling and the level at which the description is performed. Thus, complexity increases not only when new qualities are introduced into consideration, but also in the transition to a more detailed description of the process of the functioning of the modeling object, that is, the system.

We formulate the problem of applied modeling theory, proceeding from the requirements that the user (researcher, developer of system 5) will present to him, conducting experiments with the processes of functioning of 5 and its elements for solving a specific applied problem. In this context, the main task in solving management problems is to select models at the level of operational control, while retaining essential features for the SU, 5 subject to implementation constraints in the RMW (especially in operational management). In the future, the model, which is practically realized taking into account the limited resources, will be called . This way, in addition to the theoretical questions of constructing the model in general, we will consider the issues of model profitability associated with the formal representation of its description, its simplification, model, etc.

The fact that the simulated system & pound; exists only as a developer's intention, introduces significant difficulties in the development of such a theory. In particular, it is not possible to directly verify the adequacy of the model of the process of functioning of system 5 with the help of a real object. Part of this difficulty is eliminated by carrying out full-scale experiments with elements of 5. A number of significant difficulties arise from the incompleteness of the initial information about the modeling object.

The large amount of knowledge about systems and their elements accumulated to date, subject to integration within the framework of the theory of modeling and incommensurable with the cognitive capabilities of one researcher, raises the need for the organization and detailing of such knowledge (theory) in a system that involves only a very limited number of objects while maintaining the commonality of the approach. At the same time, the development of separate methods of statistical modeling, modeling languages, the theory of planning of machine experiments, etc. is insufficient.

Creating an applied theory that provides the specific needs of the model developer and embraces the entire modeling process in the broadest sense of the word requires a systematic approach and, first of all, the establishment of the foundations of the theory: concepts about the object, subject, content, structure and logic of the theory.

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