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Fuller singularities for generic control-affine systems with an even number of controls

Abstract : In this article we study how bad can be the singularities of a time-optimal trajectory of a generic control affine system. In the case where the control is scalar and belongs to a closed interval it was recently shown in [6] that singularities cannot be, generically, worse than finite order accumulations of Fuller points, with order of accumulation lower than a bound depending only on the dimension of the manifold where the system is set. We extend here such a result to the case where the control has an even number of scalar components and belongs to a closed ball.
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Submitted on : Friday, February 21, 2020 - 9:10:08 AM
Last modification on : Tuesday, September 28, 2021 - 5:16:08 PM
Long-term archiving on: : Friday, May 22, 2020 - 2:29:41 PM

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Francesco Boarotto, Yacine Chitour, Mario Sigalotti. Fuller singularities for generic control-affine systems with an even number of controls. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2020, 58 (2), pp.1207-1228. ⟨10.1137/19M1285305⟩. ⟨hal-02276960v2⟩

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