  This paper concerns optimal control problems for a class of sweeping
processes governed by discontinuous unbounded differential inclusions that are
described via normal cone mappings to controlled moving sets. Largely motivated
by applications to hysteresis, we consider a general setting where moving sets
are given as inverse images of closed subsets of finite-dimensional spaces
under nonlinear differentiable mappings dependent on both state and control
variables. Developing the method of discrete approximations and employing
generalized differential tools of first-order and second-order variational
analysis allow us to derive nondegenerated necessary optimality conditions for
such problems in extended Euler-Lagrange and Hamiltonian forms involving the
Hamiltonian maximization. The latter conditions of the Pontryagin Maximum
Principle type are the first in the literature for optimal control of sweeping
processes with control-dependent moving sets.
