Maximum-Hands-Off Control and L1 Optimality

Abstract

In this article, we propose a new paradigm of control, called a maximum-hands-off control. A hands-off control is defined as a control that has a much shorter support than the horizon length. The maximum-hands-off control is the minimum-support (or sparsest) control among all admissible controls. We first prove that a solution to an L1-optimal control problem gives a maximum-hands-off control, and vice versa. This result rationalizes the use of L1 optimality in computing a maximum-hands-off control. The solution has in general the "bang-off-bang" property, and hence the control may be discontinuous. We then propose an L1/L2-optimal control to obtain a continuous hands-off control. Examples are shown to illustrate the effectiveness of the proposed control method.

2013 IEEE 52nd Annual Conference on Decision and Control (CDC)

Cited by in corpus (6)

• Maximum Hands-Off Control: A Paradigm of Control Effort Minimization
• Characterization of maximum hands-off control
• Hands-Off Control as Green Control
• Input Novelty as a Control Metric for Time Varying Linear Systems
• Maximum Hands-off Control without Normality Assumption
• Continuity of the Value Function in Sparse Optimal Control