Optimal Control of Sweeping Processes with Nonsmooth Moving Sets: A Numerical Algorithm

Abstract

This paper extends the numerical method introduced by de Pinho et al. [22] and later developed in Nour and Zeidan [33, 37] to the nonautonomous case where the nonsmooth sweeping set depends explicitly on time. The moving character of the sweeping set creates substantial additional difficulties, since several geometric constants involved in the analysis may a priori depend on time. To overcome this issue, we establish uniform geometric estimates for the moving constraint sets and their boundaries. These estimates allow us to extend the discrete approximation scheme developed in [22, 33, 37] and prove its convergence toward admissible solutions of the original problem. Several examples illustrating the applicability of the proposed method are also presented.