Optimal control and feedback control for nonlinear impulsive evolutionary equations

Abstract

The aim of this paper is to study the existence, optimal control and feed-back 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 feed-back control system by establishing several sufficient assumptions. An application on a quasistatic frictional contact problem is provided.