A sparsity-based Fokker-Planck optimal control framework for modeling traffic flows

• Published in: AIP conference proceedings Vol. 2302; no. 1
• Main Author: Roy, S.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Melville American Institute of Physics 03.12.2020
• Subjects: Fokker-Planck equation; Optimal control; Optimization; Probability density functions; Stochastic models; Stochastic processes; Traffic control; Traffic flow; Traffic models
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0033514

A new Fokker-Planck control framework is presented to control the spread and flow of traffic motion that is modeled using a stochastic process. This framework is based on the minimization of an expectation functional subject to a Fokker-Planck equation that models the evolution of the probability density function of the underlying stochastic process. The Fokker-Planck equation comprises of sparse bilinear optimal controls for the flow and spread of the stochastic process. Theoretical results on existence of optimal controls was derived. A new and efficient scheme for solving the Fokker-Planck equation was also presented that is conservative, positive, stable, second order accurate, that can be easily extended to higher dimensions. Numerical results of controlled motion of traffic along trajectories containing obstacles demonstrated the effectiveness of the proposed framework.