  The paper concerns the study and applications of a new class of optimal
control problems governed by a perturbed sweeping process of the hysteresis
type with control functions acting in both play-and-stop operator and additive
perturbations. Such control problems can be reduced to optimization of
discontinuous and unbounded differential inclusions with pointwise state
constraints, which are immensely challenging in control theory and prevent
employing conventional variation techniques to derive necessary optimality
conditions. We develop the method of discrete approximations married with
appropriate generalized differential tools of modern variational analysis to
overcome principal difficulties in passing to the limit from optimality
conditions for finite-difference systems. This approach leads us to
nondegenerate necessary conditions for local minimizers of the controlled
sweeping process expressed entirely via the problem data. Besides illustrative
examples, we apply the obtained results to an optimal control problem
associated with of the crowd motion model of traffic flow in a corridor, which
is formulated in this paper. The derived optimality conditions allow us to
develop an effective procedure to solve this problem in a general setting and
completely calculate optimal solutions in particular situations.
