$L^1$-Minimization for Mechanical Systems
Optimization and Control
2015-12-18 v2
Abstract
Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the -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 -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.
Cite
@article{arxiv.1506.00569,
title = {$L^1$-Minimization for Mechanical Systems},
author = {Zheng Chen and Jean-Baptiste Caillau and Yacine Chitour},
journal= {arXiv preprint arXiv:1506.00569},
year = {2015}
}