Maximum Hands-Off Control: A Paradigm of Control Effort Minimization

Abstract

In this paper, we propose a paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon continuous-time control, we show the equivalence between the maximum hands-off control and L1-optimal control under a uniqueness assumption called normality. This result rationalizes the use of L1 optimality in computing a maximum hands-off control. The same result is obtained for discrete-time hands-off control. We also propose an L1/L2-optimal control to obtain a smooth hand..