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arXiv · 1307.8232

Maximum-Hands-Off Control and L1 Optimality

Masaaki Nagahara·Daniel E. Quevedo·Dragan Nesic
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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.

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Masaaki Nagahara, Daniel E. Quevedo, Dragan Nesic. 2013-07-31. Maximum-Hands-Off Control and L1 Optimality. https://arxiv.org/abs/1307.8232

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