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.
Domaines
Optimisation et contrôle [math.OC]| Origine | Fichiers produits par l'(les) auteur(s) |
|---|---|
| Licence |
