Design of Sparse Control With Minimax Concave Penalty

Abstract

In this paper, we propose a novel computational method for sparse control, also known as maximum hands-off control, using the minimax concave penalty. The sparse control problem is formulated as an L0-optimal control problem, which is known to be hard to solve. To overcome this difficulty, we propose using the minimax concave penalty as a surrogate for the L0 norm. We demonstrate the equivalence between the original and proposed control problems without relying on the normality assumption, which is typically required when approximating the L0 norm with the L1 norm. Furthermore, we present an effective numerical algorithm for the proposed optimal control based on the Alternating Direction Method of Multipliers (ADMM). A design example is shown to illustrate the effectiveness of the proposed method.