# Unbounded Viscosity Solutions of Hybrid Control Systems

Abstract : We study a hybrid control system in which both discrete and continuous controls are involved. The discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set $A$ or a controlled jump set $C$ where controller can choose to jump or not. At each jump, trajectory can move to a different Euclidean space. We allow the cost functionals to be unbounded with certain growth and hence the corresponding value function can be unbounded. We characterize the value function as the unique viscosity solution of the associated quasivariational inequality in a suitable function class. We also consider the evolutionary, finite horizon hybrid control problem with similar model and prove that the value function is the unique viscosity solution in the continuous function class while allowing cost functionals as well as the dynamics to be unbounded.
keyword :
Type de document :
Article dans une revue
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2010, 16 (01), pp.176--193. 〈10.1051/cocv:2008076〉
Domaine :
Liste complète des métadonnées

Littérature citée [11 références]

https://hal.archives-ouvertes.fr/hal-00255763
Contributeur : Guy Barles <>
Soumis le : jeudi 14 février 2008 - 09:47:20
Dernière modification le : mercredi 12 décembre 2018 - 15:26:07
Document(s) archivé(s) le : jeudi 20 mai 2010 - 22:00:28

### Fichiers

unbdd_hybrid.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

Guy Barles, Sheetal Dharmatti, Mythily Ramaswamy. Unbounded Viscosity Solutions of Hybrid Control Systems. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2010, 16 (01), pp.176--193. 〈10.1051/cocv:2008076〉. 〈hal-00255763〉

### Métriques

Consultations de la notice

## 235

Téléchargements de fichiers