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 is established and local optimality conditions are derived via strong converging continuous approximations, whose state entirely resides in the interior of the prox-regular set. Consequently, subdifferentials smaller than the standard ones are now employed in the optimality results. [ABSTRACT FROM AUTHOR]