Optimal feedback control and controllability for hyperbolic evolution inclusions of Clarke's subdifferential type

In this paper, by applying the weak closedness of multi-valued maps and the properties of Clarke's subdifferential, we consider new results of optimal feedback control and controllability for hyperbolic evolution inclusions of Clarke's subdifferential type. We omit the condition that the evolution operator and the values of multi-valued map are compact. Our main results can be applied to the problems of hyperbolic partial differential equations and hemivariational inequalities.