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Time-Optimal Trajectories of Generic Control-Affine Systems Have at Worst Iterated Fuller Singularities

Abstract : We consider in this paper the regularity problem for time-optimal trajectories of a single-input control-affine system on a n-dimensional manifold. We prove that, under generic conditions on the drift and the controlled vector field, any control u associated with an optimal trajectory is smooth out of a countable set of times. More precisely, there exists an integer K, only depending on the dimension n, such that the non-smoothness set of u is made of isolated points, accumulations of isolated points, and so on up to K-th order iterated accumulations.
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https://hal.inria.fr/hal-01528205
Contributor : Mario Sigalotti Connect in order to contact the contributor
Submitted on : Friday, May 18, 2018 - 5:02:26 PM
Last modification on : Thursday, June 9, 2022 - 3:41:06 AM
Long-term archiving on: : Tuesday, September 25, 2018 - 2:59:53 PM

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  • HAL Id : hal-01528205, version 3
  • ARXIV : 1705.10055

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Francesco Boarotto, Mario Sigalotti. Time-Optimal Trajectories of Generic Control-Affine Systems Have at Worst Iterated Fuller Singularities. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019, 36 (2), pp.327-346. ⟨hal-01528205v3⟩

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