Optimal feedback control for a class of second-order evolution differential inclusions with Clarke’s subdifferential

. The goal of this paper is to study optimal feedback control for a class of non-autonomous second-order evolution inclusions with Clarke’s subdifferential in a separable reflexive Banach space. We only assume that the second order evolution operator involved satisfies the strong continuity condition instead of the compactness, which was used in previous literature. By using the properties of multimaps and Clarke’s subdifferential, we assume some sufficient conditions to ensure the existence of feasible pairs of the feedback control systems. Furthermore, we also prove the existence of optimal control pairs