Asymptotic behavior of an optimal control system with two small singularly excitatory parameters

Abstract

The subject of research in the article is dynamic control systems with optimal slow motions. The goal of the work is to obtain an asymptotic approximation of the control in the form of feedback, which, not being uniform in the domain of the system definition, forms slow motions of the system uniformly close to optimal ones. The objectives of the study are to conduct an asymptotic analysis of the controller for small values of the parameters. Applied methods: methods of minimization of quadratic functions and methods of matrix algebra. The obtained results: the problem of the optimal equation with two small singularly exciting parameters is considered. Requirements for the characteristics and controllability of the selected system have been introduced. The problem under consideration, in contrast to well-known studies, is connected with a fundamental problem: as the system parameters tend to zero, certain components of the matrix that satisfies the Ricatti equation, due to the limiting condition for it, acquire singularities in certain time intervals. The practical significance of the work lies in the fact that with the use of minimization methods, general methods are obtained for constructing a uniform region of asymptotics for optimal control systems with two small singular-exciting parameters with respect to another small parameter.