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.
Keywords
Cite
@article{arxiv.1307.8232,
title = {Maximum-Hands-Off Control and L1 Optimality},
author = {Masaaki Nagahara and Daniel E. Quevedo and Dragan Nesic},
journal= {arXiv preprint arXiv:1307.8232},
year = {2013}
}
Comments
2013 IEEE 52nd Annual Conference on Decision and Control (CDC)