Optimal Feedback Control Problem for a Singularly Perturbed Discrete System

被引：7

作者：

Yuldashev, T. K. ^{[1
]}

Ashirbaev, B. Y. ^{[2
]}

机构：

[1] Tashkent State Univ Econ, Dept Gen & Math Sci, Tashkent 100066, Uzbekistan

[2] Kyrgyz Russian Slavian Univ, Dept Appl Math, Bishkek 720022, Kyrgyzstan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 02期

关键词：

singularly perturbed discrete system; small step; quadratic functional; transition matrix; Riccati and Lyapunov difference equations;

D O I：

10.1134/S1995080223020373

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The article proposes an asymptotic method for constructing an optimal control in a linear singularly perturbed discrete system with feedback. The optimal control is constructed for an equivalent system obtained by separating the state variables of the original system. Since in the feedback problem the optimal control depends on the solution of the nonlinear difference matrix Riccati equation, this equation is transformed to three linear singularly perturbed difference equations and the asymptotics of the solutions of these equations are constructed.

引用

页码：661 / 668

页数：8

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