Maximum hands-off control and L1 optimality

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 L-optimal control problem gives a maximum-handsoff control, and vice versa. This result rationalizes the use of L 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 L/L-optimal control to obtain a continuous hands-off control. Examples are shown to illustrate the effectiveness of the proposed control method.