Some Aspects of the Synthesis of Automated Singularly Perturbed Control Systems

Researchers of numerous aspects of the implementation of optimal control over the past few decades have paid significant attention to solving problems related to the synthesis of object control systems, phenomena and processes of various nature, including such systems, the structure and content of which significantly change during their operation. Mathematical modeling of the processes of functioning of such systems, as a rule, is realized by forming systems of a large number of differential equations. At the same time, in order to ensure the quality of modeling and subsequent effective control of various objects, special attention is paid to the analysis of the properties of the set of coefficients of the above differential equations. In turn, the above circumstance necessitates a deep modernization of algorithms for solving the so-called "regular problems" of system synthesis. The purpose of this article is to develop a number of approaches and a set of algorithms that allow you to successfully synthesize adequate mathematical models of the so-called singular-perturbed systems in general, and in particular, their individual structural components. The methodology for implementing this scientific research is based on mathematical modeling and subsequent forecasting of the functioning of specific controlled objects and processes, as well as their control systems.