Linear Quadratic Tracking Control with Sparsity-Promoting Regularization

In this paper, we propose a novel linear quadratic tracking control with sparsity regularization using L-0 norm. Sparsity regularization leads to sparse control, which has a significant length of time over which the control is exactly zero. Since the L-0 cost is non-convex and discontinuous, we introduce L-1 relaxation to make the optimization numerically tractable. The numerical solution is obtained with the aid of time-discretization to derive a discrete-time optimal control problem with l(1) regularization. We also give an upper bound of the terminal state under perturbations in the initial states and the state-space matrices. Numerical examples illustrate the effectiveness of the proposed control.