# Classification of local optimal syntheses for time minimal control problems with state constraints

Abstract : This paper describes the analysis under generic assumptions of the small \textit{time minimal syntheses} for single input affine control systems in dimension $3$, submitted to \textit{state constraints}. We use geometric methods to evaluate \textit{the small time reachable set} and necessary optimality conditions. Our work is motivated by the \textit{optimal control of the atmospheric arc for the re-entry of a space shuttle}, where the vehicle is subject to constraints on the thermal flux and on the normal acceleration.
Document type :
Conference papers

https://hal.archives-ouvertes.fr/hal-00086439
Contributor : Emmanuel Trélat <>
Submitted on : Tuesday, July 18, 2006 - 6:17:44 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Friday, May 13, 2011 - 11:35:29 PM

### Identifiers

• HAL Id : hal-00086439, version 1

### Citation

Bernard Bonnard, Ludovic Faubourg, Emmanuel Trélat. Classification of local optimal syntheses for time minimal control problems with state constraints. 2003, pp.117--122. ⟨hal-00086439⟩

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