APPLICATIONS OF OPTIMAL CONTROL OF A NONCONVEX SWEEPING PROCESS TO OPTIMIZATION OF THE PLANAR CROWD MOTION MODEL

This paper concerns optimal control of a nonconvex perturbed sweeping process and its applications to optimization of the planar crowd motion model of traffic equilibria. The obtained theoretical results allow us to investigate a dynamic optimization problem for the microscopic planar crown motion model with finitely many participants and completely solve it analytically in the case of two participants.