L¹-Minimization for Mechanical Systems
Chen, Zheng · Caillau, Jean-Baptiste · Chitour, Yacine
Original · EN
Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the L¹-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 L¹-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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