A Control Space Ensuring the Strong Convergence of Continuous Approximation for a Controlled Sweeping Process

A controlled sweeping process with prox-regular set, $$W^{1,2}$$ -controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions established local optimality conditions are derived via strong converging continuous approximations, whose state entirely resides the interior set. Consequently, subdifferentials smaller than standard ones now employed results.