Time-optimal trajectories of generic control-affine systems have at worst iterated Fuller singularities
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 2, pp. 327-346.
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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.

DOI : 10.1016/j.anihpc.2018.05.005
Mots-clés : Geometric optimal control, Chattering, Fuller, Genericity 
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     author = {Boarotto, Francesco and Sigalotti, Mario},
     title = {Time-optimal trajectories of generic control-affine systems have at worst iterated {Fuller} singularities},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {327--346},
     publisher = {Elsevier},
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Boarotto, Francesco; Sigalotti, Mario. Time-optimal trajectories of generic control-affine systems have at worst iterated Fuller singularities. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 2, pp. 327-346. doi : 10.1016/j.anihpc.2018.05.005. http://www.numdam.org/articles/10.1016/j.anihpc.2018.05.005/

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