2015/06/01 by Zheng Chen, Jean‐Baptiste Caillau, Chen, Zheng +3 · 1 citation
Computer Science · Engineering · #Adaptive Control of Nonlinear Systems #Elasticity and Material Modeling #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1506.00569
openalex publication_date 2015/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.