Value function in maximum hands-off control for linear systems

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• 作者：Takuya Ikeda ^{ikeda.t@acs.i.kyoto-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Masaaki Nagahara ^{nagahara@ieee.org" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Optimal control ; Continuity ; Bang&ndash ; bang control ; Discontinuous control ; Linear systems ; Minimum-time control ; Predictive control
• 刊名：Automatica
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：64
• 期：Complete
• 页码：190-195
• 全文大小：549 K

文摘

In this brief paper, we study the value function in maximum hands-off control. Maximum hands-off control, also known as sparse control, is the L⁰$L^0$-optimal control among the feasible controls. Although the L⁰$L^0$ measure is discontinuous and non-convex, we prove that the value function, or the minimum L⁰$L^0$ norm of the control, is a continuous and strictly convex function of the initial state in the reachable set, under an assumption on the controlled plant model. We then extend the finite-horizon maximum hands-off control to model predictive control (MPC), and prove the recursive feasibility and the stability by using the continuity and convexity properties of the value function.