CAUSAL STATE FEEDBACK REPRESENTATION FOR LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS OF SINGULAR VOLTERRA INTEGRAL EQUATIONS

被引：11

作者：

Han, S. H. U. O. ^{[1
]}

Lin, P. I. N. G. ^{[1
]}

Yong, J. I. O. N. G. M. I. N. ^{[2
]}

机构：

[1] Stat Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2023年 / 13卷 / 04期

基金：

中国国家自然科学基金; 国家重点研发计划;

关键词：

Singular Volterra integral equation; quadratic optimal control; frac-tional differential equations; causal state feedback representation; FRACTIONAL OPTIMAL-CONTROL; MODEL; DISSIPATION; FORMULATION; PRINCIPLE; SCHEME;

D O I：

10.3934/mcrf.2022038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with a linear quadratic optimal control for a class of singular Volterra integral equations. Our framework covers the problems for fractional differential equations. Under some necessary convex-ity conditions, an optimal control exists, and can be characterized via Fre ' chet derivative of the quadratic functional in a Hilbert space or via maximum prin-ciple type necessary conditions. However, these (equivalent) characterizations are not causal, meaning that the current value of the optimal control depends on the future values of the optimal state. Practically, this is not feasible. We obtain a causal state feedback representation of the optimal control via a Fred -holm integral equation. Finally, a concrete form of our results for fractional differential equations is presented.

引用

页码：1282 / 1317

页数：36

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