Research Article

Optimal control and feedback control for nonlinear impulsive evolutionary equations

Published in: Quaestiones Mathematicae
Volume 47 , issue 2 , 2024 , pages: 375–398

DOI: 10.2989/16073606.2023.2228548

Author(s): Bin Yin Guangxi Minzu University, P.R. China , Biao Zeng Guangxi Minzu University, P.R. China

Keywords: 93B52 , 47J22 , 35K86 , Impulsive evolutionary equation , existence , optimal control , feedback control , weakly continuous operator

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Abstract

The aim of this paper is to study the existence, optimal control and feedback control for a class of nonlinear impulsive evolution equations involving weakly continuous operators. We first obtain the existence result of the evolution equation without impulse in any subinterval by Rothe method, and construct a solution of impulsive evolution equation by using this result. Moreover, we obtain the existence of optimal control pairs for the optimal control problem and feasible pairs for the feedback control system by establishing several suﬃcient assumptions. An application on a quasistatic frictional contact problem is provided.

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