Description of accessibility sets near an abnormal trajectory and consequences

Abstract : We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer $\gamma$ into two sectors, bordered by the first Pontryagin's cone along $\gamma$, called the $L^\infty$-sector and the $L^2$-sector. Moreover we find again necessary and sufficient conditions of optimality of an abnormal trajectory for such systems, for any optimization problem.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-00086433
Contributor : Emmanuel Trélat <>
Submitted on : Tuesday, July 18, 2006 - 6:56:00 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Tuesday, April 6, 2010 - 12:15:46 AM

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  • HAL Id : hal-00086433, version 1

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Emmanuel Trélat. Description of accessibility sets near an abnormal trajectory and consequences. 2002, pp.89--99. ⟨hal-00086433⟩

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