OPTIMAL CONTROL PROBLEMS FOR A NEUTRAL INTEGRO-DIFFERENTIAL SYSTEM WITH INFINITE DELAY

被引：14

作者：

Huang, H. A., I ^{[1
]}

Fu, Xianlong ^{[1
]}

机构：

[1] East China Normal Univ, Shanghai Key Lab PMMP, Sch Math Sci, Shanghai 200241, Peoples R China

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2022年 / 11卷 / 01期

关键词：

infinite delay; resolvent operator; optimal control; Neutral integro-differential system; EVOLUTION INCLUSIONS; RESOLVENT OPERATORS; INTEGRAL-EQUATIONS; EXISTENCE; SOLVABILITY; SPACES;

D O I：

10.3934/eect.2020107

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work devotes to the study on problems of optimal control and time optimal control for a neutral integro-differential evolution system with infinite delay. The main technique is the theory of resolvent operators for linear neutral integro-differential evolution systems constructed recently in literature. We first establish the existence and uniqueness of mild solutions and discuss the compactness of the solution operator for the considered control system. Then, we investigate the existence of optimal controls for the both cases of bounded and unbounded admissible control sets under some assumptions. Meanwhile, the existence of time optimal control to a target set is also considered and obtained by limit arguments. An example is given at last to illustrate the applications of the obtained results.

引用

页码：177 / 197

页数：21

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