Results Concerning to the Optimal Feedback Control for Second-Order Damped Evolution Inclusions with Clarke's Subdifferential Type

In this article, we investigate the optimal feedback control for a class of damping second-order evolution inclusions with Clarke's subdifferential type in a separable reflexive Banach spaces. First, the existence of a mild solution is identified for the suggested second-order differential inclusion with the notions of generalized Clarke's subdifferential type. Next, by adopting the fixed point technique of condensing multi-valued maps, the conditions for generalized Clarke's subdifferential and the cosine family are employed for the existence of a mild solution. By using Filippove theorem and the Cesari property, a new set of sufficient conditions are formulated to guarantee the existence result of feasible pairs. Furthermore, the optimal feedback control results for the given system are proven. In the end, an illustration is presented to highlight our primary findings.