 |
|
|
|
| HAL : hal-00004191, version 4 |
| arXiv : math/0502172 |
| Fiche détaillée |  Récupérer au format |
|
|
| Versions disponibles : | v1 (08-02-2005) | v2 (05-01-2006) | v3 (05-01-2006) | v4 (07-01-2008) |
|
|
|
|
| An hybrid system approach to nonlinear optimal control problems |
|
|
Jean-Guillaume Dumas 1Aude Rondepierre 2 |
|
|
| (08/02/2005) |
|
|
|
| We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced by piecewise affine approximations which allow an analytical resolution. The sequence of affine models then forms a sequence of states of a hybrid automaton. Given a sequence of states, we introduce an hybrid approximation of the nonlinear controllable domain and propose a new algorithm computing a controllable, piecewise convex approximation. The same way the nonlinear optimal control problem is replaced by an hybrid piecewise affine one. Stating a hybrid maximum principle suitable to our hybrid model, we deduce the global structure of the hybrid optimal control steering the system to the target. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Laboratoire Jean Kuntzmann (LJK) |
|
|
|
CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
|
|
| 2 : | Mathématiques pour l'Industrie et la Physique (MIP) |
|
|
|
CNRS : UMR5640 – Université des Sciences Sociales - Toulouse I – Université Paul Sabatier - Toulouse III – Institut National des Sciences Appliquées de Toulouse |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Optimisation et contrôle Informatique/Calcul formel |
|
|
| Affine and Nonlinear Optimal Control Problems – Canonical Transformation – Controllability – Hybrid System. |
|
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| hal-00004191, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00004191 | |
| oai:hal.archives-ouvertes.fr:hal-00004191 | |
| Contributeur : Jean-Guillaume Dumas | |
| Soumis le : Lundi 7 Janvier 2008, 14:57:21 | |
| Dernière modification le : Lundi 7 Janvier 2008, 15:09:56 | |
