V.A. Raikhlin1

1 Kazan National Research Technical University named after A. N. Tupolev (Kazan, Russia)

The main provisions of the author's concept of constructive systems modeling (CSM), focused on conceptual assistance in finding effective solutions to the problems of synthesis of complex systems with incomplete initial information in various fields of knowledge and in their acceptable justification, are given. Fundamental for this methodology is the concept of a mathematical model of the synthesis process as a search area for solutions with certain properties in certain spaces, the interpretation of the object of synthesis as a model of some hypothetical system, and the recognition of the legitimacy of introducing postulates in technical sciences based on accumulated experience. Analytical reviews of original studies in two polar regions – on artificial lines (AL) and associative steganography (AS) – show the efficiency of the adopted orientation. The possibility of assigning the status of a universal approach to CSM is discussed with references to original research in various fields of informatics. In the field of AL, attention is focused on the discovery of a new type of low-pass filter - the Bessel-Butterworth bipolynomial filter. In the field of AS – on a new effective method of information protection. Information about these studies was published in prestigious publications repeatedly over the course of half a century. The greatest interest was gained by the results of AS. But brought together and in sufficient detail, from the standpoint of a common methodology, analytical results in both areas can acquire a fundamentally new quality in the opinion of the scientific community.

Usually, the required determinism is achieved when the problem is formulated by introducing various kinds of definitions and restrictions. Postulates do the same thing, but declare it as patterns. Thus, in the course of research on homogeneous artificial lines, the author developed a deep inner conviction that the proposed constructive method gives solutions close to the global optimum. For basic structures of limited complexity, this has been established quite rigorously. However, as the dimension increased, the proof of optimality became an unsolvable problem. It was necessary to look for some special approach to justification. And such an approach was found. It consisted in postulating the convergence of mapping numerical sequences to some standard one in the introduced metric spaces of increasing dimension. As a result, the canonicity of the found Bessel-Butterworth filter was substantiated. The quality of assessments of the adequacy of constructive methods (the answer to the question «WHY?»), developed from the usual positions of definitions-limitations and from the positions of postulates, are significantly different. The assessment in the first case is somewhat amorphous: it is possible and so. In the second, it is categorical to the extent of the accumulated knowledge: it is necessary only in such a way that it is far from the same. In this review, the author makes another attempt to convince the «wide circle» of the prospects of a constructive approach to the synthesis of complex systems, focusing mainly on young scientific personnel – novice researchers.

Raikhlin V.A. Constructive modeling is the relevant approach to the synthesis of complex systems. Nonlinear World. 2022. V. 20. № 4. 2022. P. 5-21. DOI: https://doi.org/10.18127/j20700970-202204-01 (In Russian)

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