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arXiv · 1705.10055

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

Francesco Boarotto·Mario Sigalotti
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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.

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Francesco Boarotto, Mario Sigalotti. 2017-05-29. Time-Optimal Trajectories of Generic Control-Affine Systems Have at Worst Iterated Fuller Singularities. https://arxiv.org/abs/1705.10055

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