A Tractable Nonconvex Surrogate for the Matrix l0-quasinorm: Applications to Sparse Feedback Design*. Issue 13 (2016)

• Record Type: Journal Article
• Authors: Bykov, A.; Shcherbakov, P.; Ding, M.
• Is Part Of: IFAC-PapersOnLine. Volume 49:Issue 13(2016)
• Page Start: 53
• Page End: 58
• Publication Date: 2016
• Subjects: linear systems -- sparse feedback -- H∞-optimization -- LMIs -- DC-functions -- CCCP; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2016.07.926
• Languages: English
• ISSNs: 2405-8963

Abstract

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.