Optimal control problem governed by a highly nonlinear singular Volterra equation: Existence of solutions and maximum principle

被引：1

作者：

Idczak, Dariusz ^{[1
,2
]}

机构：

[1] Univ Lodz, Fac Math & Comp Sci, Lodz, Poland

[2] Univ Lodz, Fac Math & Comp Sci, Lodz, Poland

来源：

OPTIMAL CONTROL APPLICATIONS & METHODS | 2024年 / 45卷 / 01期

关键词：

existence of optimal solutions; extremum principle; fractional potential; implicit function theorem for multivalued mappings; Lagrange problem; lower closure theorem; maximum principle; Volterra integral equation;

D O I：

10.1002/oca.3057

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider a Lagrange optimal control problem for a Volterra integral equation of fractional potential type. We prove a theorem on the existence of an optimal solution and derive a maximum principle. The proof of the existence theorem is based on the lower closure theorem for orientor fields due to Cesari and Filippov-type selection theorem due to Rockafellar. The proof of the maximum principle is based on an extremum principle for smooth problems proved in Idczak and Walczak (Games. 2020;11:56). We consider a Lagrange optimal control problem for a Volterra integral equation of fractional potential type and prove a theorem on the existence of an optimal solution as well as derive a maximum principle.image

引用

页码：274 / 301

页数：28

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