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In this article, we propose a new paradigm of control, called amaximum-hands-off control. A hands-off control is defined as a control that hasa much shorter support than the horizon length. The maximum-hands-off controlis the minimum-support (or sparsest) control among all admissible controls. Wefirst prove that a solution to an L1-optimal control problem gives amaximum-hands-off control, and vice versa. This result rationalizes the use ofL1 optimality in computing a maximum-hands-off control. The solution has ingeneral the "bang-off-bang" property, and hence the control may bediscontinuous. We then propose an L1/L2-optimal control to obtain a continuoushands-off control. Examples are shown to illustrate the effectiveness of theproposed control method.

Maximum-Hands-Off Control and L1 Optimality