Value function in maximum hands-off control for linear systems. (February 2016)

• Record Type: Journal Article
• Authors: Ikeda, Takuya; Nagahara, Masaaki
• Is Part Of: Automatica. Volume 64(2016)
• Page Start: 190
• Page End: 195
• Publication Date: 2016-02
• Subjects: Optimal control -- Continuity -- Bang–bang control -- Discontinuous control -- Linear systems -- Minimum-time control -- Predictive control; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2015.10.043
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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 L 0 -optimal control among the feasible controls. Although the L 0 measure is discontinuous and non-convex, we prove that the value function, or the minimum 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.