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On singularities of minimum time control-affine systems

Abstract : Affine control problems arise naturally from controlled mechanical systems. Building on previous results [2, 8], we go one step further and prove that the extremal flow given by Pontrjagin maximum principle can be stratified. We also study the regularity of this flow in terms of regular-singular transition and prove that, as in the nilpotent approximation, the singularity of time minimizing extremals is logarithmic. We finally give global bounds on the number of such singularities and apply our results to the control of two and three bodies in space mechanics.
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https://hal.inria.fr/hal-01718345
Contributor : Jean-Baptiste Caillau Connect in order to contact the contributor
Submitted on : Thursday, November 4, 2021 - 6:31:09 PM
Last modification on : Friday, November 25, 2022 - 10:12:06 AM

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Jean-Baptiste Caillau, Jacques Fejoz, Michaël Orieux, Robert Roussarie. On singularities of minimum time control-affine systems. SIAM Journal on Control and Optimization, 2022, 60 (2), pp.1143-1162. ⟨10.1137/20M1366861⟩. ⟨hal-01718345v2⟩

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