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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.inria.fr/hal-01528205
Contributeur : Mario Sigalotti <>
Soumis le : mardi 11 juillet 2017 - 09:24:39
Dernière modification le : mercredi 23 mai 2018 - 01:29:05
Document(s) archivé(s) le : mercredi 24 janvier 2018 - 17:46:26

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  • HAL Id : hal-01528205, version 2
  • 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. 2017. 〈hal-01528205v2〉

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