Optimal control of a first order Fokker-Planck equation with reaction term and density constraints

Adrien Seguret (1, 2)

1 EDF R&D OSIRIS - Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We consider a constrained optimal control of an advection-reaction partial differential equation (PDE). We prove the existence of a minimizer and we characterize the solution as the weak solution of a system of two coupled PDEs. This system is composed of a Fokker-Planck equation and of a Hamilton-Jacobi equation, similarly to systems obtained in Mean Field Games (MFG). We provide regularity results of the solutions.

Mots clés: Optimal control; optimality conditions; mean field control

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Adrien Seguret. Optimal control of a first order Fokker-Planck equation with reaction term and density constraints. 2021. ⟨hal-03353917v2⟩