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| HAL: hal-00004191, version 4 |
| arXiv: math/0502172 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2005-02-08) | v2 (2006-01-05) | v3 (2006-01-05) | v4 (2008-01-07) |
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| An hybrid system approach to nonlinear optimal control problems |
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Jean-Guillaume Dumas 1Aude Rondepierre 2 |
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| (2005-02-08) |
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| 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. |
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| 1: | Laboratoire Jean Kuntzmann (LJK) |
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CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Institut Polytechnique de Grenoble |
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| 2: | Mathématiques pour l'Industrie et la Physique (MIP) |
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CNRS : UMR5640 – Université des Sciences Sociales - Toulouse I – Université Paul Sabatier - Toulouse III – Institut National des Sciences Appliquées de Toulouse |
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| Subject | : | Mathematics/Optimization and Control Computer Science/Symbolic Computation |
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| Affine and Nonlinear Optimal Control Problems – Canonical Transformation – Controllability – Hybrid System. |
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| hal-00004191, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00004191 | |
| oai:hal.archives-ouvertes.fr:hal-00004191 | |
| From: Jean-Guillaume Dumas | |
| Submitted on: Monday, 7 January 2008 14:57:21 | |
| Updated on: Monday, 7 January 2008 15:09:56 | |
