Pontryagin-Type Maximum Principle for a Controlled Sweeping Process with Nonsmooth and Unbounded Sweeping Set

The Pontryagin-type maximum principle derived in a recent article of the authors [Optimal control of nonconvex sweeping processes with separable endpoints: Nonsmooth maximum principle for local minimizers, J. Diff. Equations 318 (2022) 113–168] for optimal control problems involving sweeping processes is generalized to the case where the sweeping set C is nonsmooth and not necessarily bounded, namely, C is the intersection of a finite number of sublevel sets of smooth functions.