Optimal feedback control for a class of fractional evolution equations with history-dependent operators

被引：28

作者：

Liu, Yongjian ^{[1
]}

Liu, Zhenhai ^{[2
]}

Peng, Sisi ^{[2
]}

Wen, Ching-Feng ^{[3
,4
]}

机构：

[1] Yulin Normal Univ, Sch Math & Stat, Yulin 537000, Guangxi, Peoples R China

[2] Guangxi Minzu Univ, Guangxi Key Lab Hybrid Computat & IC Design Anal, Nanning 530006, Guangxi, Peoples R China

[3] Kaohsiung Med Univ, Ctr Fundamental Sci, Res Ctr Nonlinear Anal & Optimizat, Kaohsiung 80708, Taiwan

[4] Kaohsiung Med Univ Hosp, Dept Med Res, Kaohsiung 80708, Taiwan

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2022年 / 25卷 / 03期

关键词：

Optimal feedback control; History-dependent operators; Fractional order derivatives; Feasible pair; VARIATIONAL-INEQUALITIES; HEMIVARIATIONAL INEQUALITIES; SENSITIVITY-ANALYSIS; CONTROL-SYSTEMS; PROBLEMS DRIVEN; CONTROLLABILITY;

D O I：

10.1007/s13540-022-00054-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we will study optimal feedback control problems derived by a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. We firstly introduce suitable hypotheses to prove the existence and uniqueness of mild solutions for this kind of Riemann-Liouville fractional evolution equations with history-dependent operators. Then, by introducing a feedback iterative technique and applying Filippov theorem, we show the existence of feasible pairs and optimal control pairs of the optimal feedback control systems with history-dependent operators. Finally, we give some applications to illustrate our main results.

引用

页码：1108 / 1130

页数：23

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