A monotonic algorithm for the optimal control of the Fokker-Planck equation

Guillaume Carlier (1) , Julien Salomon (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Motivated by some crowd motion models in the presence of noise, we consider an optimal control problem governed by the Fokker-Planck equation. We sketch optimality conditions by means of an Hamilton-Jacobi-Bellman equation and we give a monotonic scheme for the numerical approximation of the solution.

Mots clés: optimal control; monotonic scheme; Fokker-Planck equation; transport

Domaines: Optimisation et contrôle [math.OC]

Guillaume Carlier, Julien Salomon. A monotonic algorithm for the optimal control of the Fokker-Planck equation. Proceedings of the 47th IEEE Conference on Decision and Control., Dec 2008, Cancun, Mexico. ⟨hal-00267432⟩