Title: 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.