Applications of Controlled Sweeping Processes to Nonlinear Crowd Motion Models with Obstacles

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.