A Maximum Principle for Optimal Control Problems involving Sweeping Processes with a Nonsmooth Set

Abstract

We generalize a Maximum Principle for optimal control problems involving sweeping systems previously derived in ``Necessary conditions for optimal control problems with sweeping systems and end point constraints'', by de Pinho, Ferreira and Smirnov, Optimization, N. 71, 11, 2022, to cover the case where the moving set may be nonsmooth. Noteworthy, we consider problems with constrained end point. A remarkable feature of our work is that we rely upon an ingenious smooth approximating family of standard differential equations in the vein of that used in ``Optimal Control involving Sweeping Processes'', by de Pinho, Ferreira and Smirnov, Set-Valued Var. Anal 27, 2019.