Study of Mathematical Models of Dynamic Systems


It becomes necessary to describe (model) properties of a stochastic object when solving various problems of analysis and synthesis for control systems majority of modern technological, economic, biological and other objects. It is necessary to develop control systems are complex, multi-element stochastic objects for them. Linear dynamic systems (LDS) are a dominant link in the research chain. They are associated with various tasks, both regulation and control. Recently, a problem of mathematical modeling becomes essential due to the increasing need to create various control systems, as well as control systems. Nowadays, there exist some methods of mathematical models building. The efficiency of each method depends on the type of a particular problem. Therefore, one of the key problems in this field is an adequate model building, i.e., particularly versatile and simple. The authors consider a non-parametric approach to building a mathematical model of LDS based on the Duhamel integral applying stochastic approximations. The paper considers a problem of non-parametric identification and building mathematical models of stationary linear dynamic objects with delay under non-parametric uncertainty. The study of a specific class of objects with a sufficiently high degree of inertia is also carried out. The paper examines a situation when it is necessary to build a mathematical model of an object in an unstable state at the moment when observation starts.

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27 February 2023

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European Publisher



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1st Edition




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Ikonnikov, О. А., Karaseva, М. V., & Rozhnov, I. P. (2023). Study of Mathematical Models of Dynamic Systems. In P. Stanimorovic, A. A. Stupina, E. Semenkin, & I. V. Kovalev (Eds.), Hybrid Methods of Modeling and Optimization in Complex Systems, vol 1. European Proceedings of Computers and Technology (pp. 394-403). European Publisher.