REGULARITY OF THE VALUE FUNCTION AND QUANTITATIVE PROPAGATION OF CHAOS FOR MEAN FIELD CONTROL PROBLEMS - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2023

REGULARITY OF THE VALUE FUNCTION AND QUANTITATIVE PROPAGATION OF CHAOS FOR MEAN FIELD CONTROL PROBLEMS

Résumé

We investigate a mean field optimal control problem obtained in the limit of the optimal control of large particle systems with forcing and terminal data which are not assumed to be convex. We prove that the value function, which is known to be Lipschitz continuous but not of class C 1 , in general, without convexity, is actually smooth in an open and dense subset of the space of times and probability measures. As a consequence, we prove a new quantitative propagation of chaos-type result for the optimal solutions of the particle system starting from this open and dense set.
Fichier principal
Vignette du fichier
PropagChaos20220401.pdf (394.89 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03628406 , version 1 (02-04-2022)

Identifiants

Citer

Pierre Cardaliaguet, Panagiotis Souganidis. REGULARITY OF THE VALUE FUNCTION AND QUANTITATIVE PROPAGATION OF CHAOS FOR MEAN FIELD CONTROL PROBLEMS. Nonlinear Differential Equations and Applications, 2023, 30 (2), pp.25. ⟨10.1007/s00030-022-00823-x⟩. ⟨hal-03628406⟩
29 Consultations
51 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More