A Maximum Principle for the Controlled Sweeping Process

We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone, and derive necessary optimality conditions of Pontryagin’s Maximum Principle type. The results are also discussed through an example. We combine techniques from Sene and Thibault (2014) and from Brokate and Krejci (2013), the latter in particular dealing with a different but related control problem. Our assumptions include the smoothness of the boundary of the moving set C(t), but, differently from Brokate and Krejci, do not require strict convexity and time independence of C(t). Rather, a kind of inward/outward pointing condition is assumed on the reference optimal trajectory at the times where the boundary of C(t) is touched. The state space is finite dimensional.