Discrete-time hands-off control by sparse optimization

Abstract

Maximum hands-off control is a control mechanism that maximizes the length of the time duration on which the control is exactly zero. Such a control is important for energy-aware control applications, since it can stop actuators for a long duration and hence the control system needs much less fuel or electric power. In this article, we formulate the maximum hands-off control for linear discrete-time plants by sparse optimization based on the ℓ1 norm. For this optimization problem, we derive an efficient algorithm based on the alternating direction method of multipliers (ADMM). We also give a model predictive control formulation, which leads to a robust control system based on a state feedback mechanism. Simulation results are included to illustrate the effectiveness of the proposed control method.