<p>The primary objective of this manuscript is to develop a systematic framework for the optimal feedback control for a class of damping second-order neutral impulsive non-autonomous evolution inclusions with Clarke’s subdifferential type in Hilbert spaces. First, the theory of strongly continuous cosine families and fixed point theorems of multivalued maps are utilized to show mild solutions for second-order evolution systems. The proposed problem formulates by considering systems with non smooth and non convex behavior, while incorporating the nature of impulses. To effectively model these dynamics, space of piecewise continuous functions is defined, and then enables a precise representation of such systems. The problem is formulated using hemivariational inequalities, and then it is helpful for offering a robust and comprehensive framework to address the complexities associated with nonconvex and nonsmooth dynamics. To prove the existence of a mild solution for the proposed system, sufficient conditions are established by employing fixed point theorem for the multivalued maps, generalized Clarke’s subdifferential type. Subsequently, we propose a new set of sufficient conditions, employing Filippov theorem and the Cesari property, to guarantee the existence of feasible pairs in feedback control systems. Finally, an application is provided to illustrate the key outcomes of our study.</p>