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Singular trajectories of driftless and control-affine systems

Abstract : We establish generic properties for singular trajectories, first for driftless, and then for control-affine systems. We show that, generically -- for the Whitney topology -- nontrivial singular trajectories are of minimal order and of corank one. As a consequence, if the number of vector fields of the system is greater than or equal to 3, then there exists generically no singular minimizing trajectory.
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https://hal.archives-ouvertes.fr/hal-00086464
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Submitted on : Tuesday, July 18, 2006 - 6:11:51 PM
Last modification on : Friday, December 3, 2021 - 11:34:08 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 12:16:11 AM

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Yacine Chitour, Frédéric Jean, Emmanuel Trélat. Singular trajectories of driftless and control-affine systems. 44th IEEE Conference on Decision and Control, Dec 2005, seville, Spain. 6 p., ⟨10.1109/cdc.2005.1582278⟩. ⟨hal-00086464⟩

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