OPTIMAL FEEDBACK CONTROL FOR SECOND-ORDER EVOLUTION EQUATIONS

Cuiyun Shi; Maojun Bin; Yunxiang Li

doi:10.11948/20200474

2022 Volume 12 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(4): 1308-1327

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Cuiyun Shi, Maojun Bin, Yunxiang Li. OPTIMAL FEEDBACK CONTROL FOR SECOND-ORDER EVOLUTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1308-1327. doi: 10.11948/20200474

Citation:

Cuiyun Shi, Maojun Bin, Yunxiang Li. OPTIMAL FEEDBACK CONTROL FOR SECOND-ORDER EVOLUTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1308-1327. doi: 10.11948/20200474

OPTIMAL FEEDBACK CONTROL FOR SECOND-ORDER EVOLUTION EQUATIONS

1.
School of Basic Science, Guilin University of Technology at Nanning, 530001 Nanning, Guangxi Province, China
2.
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, 537000 Yulin, Guangxi Province, China
3.
College of Science, Hunan City University, 413000 Yiyang, Hunan Province, China

Corresponding author: Email: bmj1999@163.com(M. J. Bin)
Fund Project: The authors were supported by NSF of Guangxi Grant (Nos. 2020GXNSFAA159152, 2020GXNSFBA297142, 2021GXNSFAA220130, 2022GXNSFAA035617)

Abstract

Abstract

The goal of this paper is to provide systematic approaches to study new results of optimal feedback control for second-order evolution equations. We firstly give some existence results of mild solutions for the equations by applying the Banach's fixed point theorem and the Leray-Schauder alternative fixed point theorem with Lipschitz conditions and different types of boundedness conditions. Next, by using the Filippove theorem and the Cesari property, a new set of sufficient assumptions are formulated to guarantee the existence results of feasible pairs for the feedback control systems. Finally, we apply our main results to the problems of controllability, Clarke's subdifferential inclusions and differential variational inequalities.
- Optimal feedback control /
- second-order evolution equation /
- existence /
- feasible pairs /
- Cesari property
MSC: 49J15, 47J20, 93B52

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References

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