Computation of maximum hands-off control

Abstract

Maximum hands-off control is a control that has the minimum L0 norm among all feasible controls. So far, we have proved that the maximum hands-off control is equivalent to the L1-optimal control under the normality assumption and is in general equivalent to the Lp-optimal control with 0 <; p <; 1. In this paper, by utilizing these results we give a numerical optimization method for the maximum hands-off control. We adopt a time discretization approach. As the complexity of the approximated problem then grows exponentially, we instead solve the equivalent L1 or Lp-optimization. Under the normality assumption we apply the alternating direction method of multipliers (ADMM) for the maximum hands-off control, and otherwise we apply the successive linearization algorithm (SLA).