Viscosity solutions of centralized control problems in measure spaces - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Viscosity solutions of centralized control problems in measure spaces

Résumé

This work focuses on a control problem in the Wasserstein space of probability measures over Rd. Our aim is to link this control problem to a suitable Hamilton-Jacobi-Bellman (HJB) equation. We explore a notion of viscosity solution using test functions that are locally Lipschitz and locally semiconvex or semiconcave functions. This regularity allows to define a notion of viscosity and a Hamiltonian function relying on directional derivatives. Using a generalization of Ekeland's principle, we show that the corresponding HJB equation admits a comparison principle, and deduce that the value function is the unique solution in this viscosity sense. The PDE tools are developed in the general framework of Measure Differential Equations.
Fichier principal
Vignette du fichier
Jerhaoui_Prost_Zidani.pdf (354.46 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY - Paternité

Dates et versions

hal-04335852 , version 1 (11-12-2023)

Identifiants

  • HAL Id : hal-04335852 , version 1

Citer

Othmane Jerhaoui, Averil Prost, Hasnaa Zidani. Viscosity solutions of centralized control problems in measure spaces. 2023. ⟨hal-04335852⟩
60 Consultations
43 Téléchargements

Partager

Gmail Facebook X LinkedIn More