  This paper is devoted to the study of the dynamic optimization of several
controlled crowd motion models in the general planar settings, which is an
application of a class of optimal control problems involving a general
nonconvex sweeping process with perturbations. A set of necessary optimality
conditions for such optimal control problems involving the crowd motion models
with multiple agents and obstacles is obtained and analyzed. Several effective
algorithms based on such necessary optimality conditions are proposed and
various nontrivial illustrative examples together with their simulations are
also presented.
