  The paper is devoted to deriving necessary optimality conditions in a general
optimal control problem for dynamical systems governed by controlled sweeping
processes with hard-constrained control actions entering both polyhedral moving
sets and additive perturbations. By using the first-order and mainly
second-order tools of variational analysis and generalized differentiation, we
develop a well-posed method of discrete approximations, obtain optimality
conditions for solutions to discrete-time control systems, and then establish
by passing to the limit verifiable necessary optimality conditions for local
minimizers of the original controlled sweeping process that are expressed
entirely in terms of its given data. The efficiency of the obtained necessary
optimality conditions for the sweeping dynamics is illustrated by solving three
nontrivial examples of their own interest.
