A class of delay evolution hemivariational inequalities and optimal feedback controls

Abstract

In this paper, we study the feedback optimal control for a class of evolution hemivariational inequalities with delay. First, we obtain the existence of feasible pairs by applying the Cesari property, the Filippov theorem, the properties of Clarke subdifferential and a fixed point theorem for multivalued maps. Next, the results of optimal feedback control pairs and time optimal control for delay evolution hemivariational inequalities are presented under sufficient conditions. Finally, an example is included to illustrate our main results.