Mean field approximation of an optimal control problem for the continuity equation arising in smart charging

Adrien Seguret (1, 2, 3)

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
3 FiME Lab - Laboratoire de Finance des Marchés d'Energie

We consider the optimal control of a finite population of hybrid processes (namely agents state is composed of a discrete and a continuous variable), modeling the optimal charging of a large population of identical plug-in electric vehicles (PEVs). We prove the convergence of the solution and that of the value of a sequence of finite population problems respectively to a solution and the value of a mean field optimal control problem.

Mots clés: Optimal control; hybrid state space; mean-field limit

Domaines: Optimisation et contrôle [math.OC]; Energie électrique

Adrien Seguret. Mean field approximation of an optimal control problem for the continuity equation arising in smart charging. Applied Mathematics and Optimization, 2023, 88 (3), pp.Article 79. ⟨10.1007/s00245-023-10054-w⟩. ⟨hal-03910634v2⟩