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Article Dans Une Revue Annales de l'Institut Henri Poincaré C, Analyse non linéaire Année : 2019

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

Résumé

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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Dates et versions

hal-01528205 , version 1 (28-05-2017)
hal-01528205 , version 2 (11-07-2017)
hal-01528205 , version 3 (18-05-2018)

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Citer

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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