A Tractable Nonconvex Surrogate for the Matrix l0-quasinorm: Applications to Sparse Feedback Design

Abstract

In Polyak et al. (2013a), an approach to sparse feedback design in linear control systems was proposed, leading to row/column sparse controller gain matrices, i.e., those containing zero rows/columns. To solve this problem, a special matrix norm was considered such that it was used as a convex surrogate for the inherently nonconvex original problem. The contribution of this current paper is twofold. First, we propose a different surrogate which shows itself more efficient, though also being nonconvex. Second, we extend the original approach toward the classical H∞-optimization problem. A heuristic in support of the efficiency of the new surrogate is given and numerical examples are presented that testify to a better performance of the new method.