Solution stability to parametric distributed optimal control problems with finite unilateral constraints

Nguyen Hai Son

doi:10.3934/eect.2021047

Article Contents

2022, Volume 11, Issue 4: 1357-1372. Doi: 10.3934/eect.2021047

This issue Previous Article Telegraph systems on networks and port-Hamiltonians. I. Boundary conditions and well-posedness Next Article The method of extremal shift in control problems for evolution variational inequalities under disturbances

Solution stability to parametric distributed optimal control problems with finite unilateral constraints

Nguyen Hai Son^,

School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, No.1 Dai Co Viet, Hanoi, Vietnam

^* Corresponding author: Nguyen Hai Son
^* Corresponding author: Nguyen Hai Son

Received: February 28, 2021

Revised: May 31, 2021

Early access: August 2021

Published: August 2022

The research is funded by Vietnam National Foundation for Scienceand Technology Development (NAFOSTED) under Grant Number 101.01-2019.308

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Abstract

This paper deals with stability of solution map to a parametric control problem governed by semilinear elliptic equations with finite unilateral constraints, where the objective functional is not convex. By using the first-order necessary optimality conditions, we derive some sufficient conditions under which the solution map is upper semicontinuous with respect to parameters.

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Mathematics Subject Classification: 49K20, 49K40, 90C31.

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References

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