Time-optimal trajectories of generic control-affine systems have at worst iterated Fuller singularities |
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Authors: | Francesco Boarotto Mario Sigalotti |
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Affiliation: | 1. Laboratorie Jacques-Louis Lions, Sorbonne Université, Université Paris-Diderot SPC, CNRS, Inria, France;2. Inria & Laboratorie Jacques-Louis Lions, Sorbonne Université, Université Paris-Diderot SPC, CNRS, Inria, France |
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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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Keywords: | Geometric optimal control Chattering Fuller Genericity |
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