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.
Cite this article
Francesco Boarotto, Mario Sigalotti, Time-optimal trajectories of generic control-affine systems have at worst iterated Fuller singularities. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, pp. 327–346DOI 10.1016/J.ANIHPC.2018.05.005