2013/07/31 by Nagahara, Masaaki, Quevedo, Daniel E., Nesic, Dragan
#FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Information Theory (cs.IT) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1307.8232
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.