ABSTRACT

A Fokker–Planck control approach to model crowd motion is investigated. This strategy is formulated as a bilinear optimal control-constrained problem governed by the Fokker–Planck equation modeling the evolution of the probability density function of the stochastic motion of the crowd. Theoretical results on existence and regularity of controls are provided. For computational purposes, the resulting optimality system is discretized using an alternate-direction implicit Chang–Cooper scheme that guarantees conservativeness, positivity,L² stability, and second-order accuracy of the forward solution. A projected non-linear conjugate gradient scheme is used to solve the optimality system. Results of numerical experiments demonstrate the efficiency of the proposed control framework.