  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 M. Sene, L. Thibault, Journal of Nonlinear and Convex Analysis 15 (2014)
and from M. Brokate and P. Krejci, Discrete and continuous dynamical systems
series B. Volume 18 (2013), 331-348, which in particular deals with a different
but related control problem. Our assumptions include the smoothness of the
boundary of the moving set $C(t)$, but do not require its strict convexity.
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.
