Optimal control of feedback control systems governed by hemivariational inequalities

This paper is mainly concerned with the feedback control systems governed by evolution hemivariational inequalities. By using the properties of multimaps and Clarke’s subdifferential, we formulate some sufficient conditions to guarantee the existence result of feasible pairs of the feedback control systems. We also present an existence result of optimal control pairs for an optimal control problem. We emphasize that our results cannot be obtained straightforwardly from the previous works.