L$^1$-minimization for mechanical systems

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. Keywords. L 1-minimization, second order mechanical systems, order two singular trajectories, no-fold conditions for broken extremals, two-body problem MSC classification. 49K15, 70Q05
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SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 54 (3), pp.1245-1265. <10.1137/15M1013274>
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Dernière modification le : samedi 18 février 2017 - 01:09:44

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Zheng Chen, Jean-Baptiste Caillau, Yacine Chitour. L$^1$-minimization for mechanical systems. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 54 (3), pp.1245-1265. <10.1137/15M1013274>. <hal-01136676>

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