Discontinuous solutions of Hamilton-Jacobi-Bellman equation under state constraints

Hélène Frankowska 1 Marco Mazzola 1
1 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
Abstract : This article is devoted to the Hamilton-Jacobi partial differential equation tV=Htx−xV V(1x)=g(x) on on [01] where the Hamiltonian H:[01]RnRnR is convex and positively homogeneous with respect to the last variable, Rn is open and g:RnR+ is lower semicontinuous. Such Hamiltonians do arise in the optimal control theory. We apply the method of generalized characteristics to show uniqueness of lower semicontinuous solution of this first order PDE. The novelty of our setting lies in the fact that we do not ask regularity of the boundary of Ω and extend the Soner inward pointing condition in a nontraditional way to get uniqueness in the class of lower semicontinuous functions.
Type de document :
Article dans une revue
Calculus of Variations and Partial Differential Equations, Springer Verlag, 2013, 46, pp.725-747. 〈10.1007/s00526-012-0501-8〉
Liste complète des métadonnées

https://hal.inria.fr/hal-00710717
Contributeur : Estelle Bouzat <>
Soumis le : jeudi 21 juin 2012 - 15:17:47
Dernière modification le : jeudi 11 janvier 2018 - 06:20:24

Identifiants

Citation

Hélène Frankowska, Marco Mazzola. Discontinuous solutions of Hamilton-Jacobi-Bellman equation under state constraints. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2013, 46, pp.725-747. 〈10.1007/s00526-012-0501-8〉. 〈hal-00710717〉

Partager

Métriques

Consultations de la notice

356