  This paper mainly focuses on solving the dynamic optimization of the planar
controlled crowd motion models with obstacles which is an application of a
class of optimal control problems governed by a general perturbed nonconvex
sweeping process. This can be considered as a significant extension of the
previous work regarding the controlled crowd motion models, where the obstacles
have not been considered. The necessary optimality conditions for the problem
under consideration are established and illustrated by a nontrivial example of
practical importance.
