# American Institute of Mathematical Sciences

August  2019, 24(8): 4191-4216. doi: 10.3934/dcdsb.2019078

## Applications of optimal control of a nonconvex sweeping process to optimization of the planar crowd motion model

 1 Department of Applied Mathematics and Statistics, State University of New York–Korea, Yeonsu-Gu, Incheon 21985, Republic of Korea, Springfield, MO 65801-2604, USA 2 Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA 3 RUDN University, Moscow 117198, Russia

Received  February 2018 Revised  October 2018 Published  April 2019

Fund Project: Research of this author was partly supported by the MSIT (Ministry of Science and ICT), Korea, under the ICT Consilience Creative Program (IITP-2017-R0346-16-1007) supervised by the IITP (Institute for Information & Communications Technology Promotion).
Research of this author was partly supported by the US National Science Foundation under grant DMS-1512846, by the US Air Force Office of Scientific Research under grant #15RT0462, and by the RUDN University Program 5-100.

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.

Citation: Tan H. Cao, Boris S. Mordukhovich. Applications of optimal control of a nonconvex sweeping process to optimization of the planar crowd motion model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4191-4216. doi: 10.3934/dcdsb.2019078
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