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arXiv · 1506.00569

$L^1$-Minimization for Mechanical Systems

Zheng Chen·Jean-Baptiste Caillau·Yacine Chitour
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Abstract

Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the $L^1$-norm of the control is addressed. An analysis of the extremal flow emphasizes the role of singular trajectories of order two [25,29]; the case of the two-body potential is treated in detail. In $L^1$-minimization, regular extremals are associated with controls whose norm is bang-bang; in order to assess their optimality properties, sufficient conditions are given for broken extremals and related to the no-fold conditions of [20]. An example of numerical verification of these conditions is proposed on a problem coming from space mechanics.

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Zheng Chen, Jean-Baptiste Caillau, Yacine Chitour. 2015-06-01. $L^1$-Minimization for Mechanical Systems. https://arxiv.org/abs/1506.00569

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