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Lower semicontinuous solutions to Hamilton-Jacobi-Bellman equations

Frankowska, Halina (1993), Lower semicontinuous solutions to Hamilton-Jacobi-Bellman equations, SIAM Journal on Control and Optimization, 31, 1, p. 257-272. http://dx.doi.org/10.1137/0331016

Type
Article accepté pour publication ou publié
Date
1993
Nom de la revue
SIAM Journal on Control and Optimization
Volume
31
Numéro
1
Éditeur
SIAM
Pages
257-272
Identifiant publication
Métadonnées
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Auteur(s)
Frankowska, Halina
Résumé (EN)
The value function of Mayer’s problem arising in optimal control is investigated, and lower semicontinuous solutions of the associated Hamilton–Jacobi–Bellman equation are defined in three (equivalent) ways. Under quite weak assumptions about the control system, the value function is the unique solution. Moreover, it is stable with respect to perturbations of the control system and the cost. It coincides with the viscosity solution whenever it is continuous.
Mots-clés
Hamilton–Jacobi equation; Mayer’s problem; viability theory; viscosity solution