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UBS, 2017, Issue 68, Pages 47–73 (Mi ubs922)  

This article is cited in 1 scientific paper (total in 1 paper)

Analysis and Synthesis of Control Systems

Numerical study on effectiveness of surrogates for the matrix $l_0$-quasinorm applied to sparse feedback design

A. Bykova, P. S. Shcherbakovab

a Institute of Control Sciences of RAS, Moscow
b Federal Research Center Informatics and Control of Russian Academy of Science

Abstract: Optimal control problem formulations sometimes require the resulting controller to be sparse, i.e. to contain zero elements in gain matrix. On the one hand, sparse feedback leads to the performance drop if compared with the optimal control, on the other hand, it confers useful properties to the system. For instance, sparse controllers allow to design distributed systems with decentralized feedback. Some sparse formulations require gain matrix of the controller to have special sparse structure, which is characterized by the occurence of zero rows in a matrix. In this paper various approximations to the number of nonzero rows of a matrix are considered to be applied to sparse feedback design in optimal control problems for linear systems. Along with a popular approach based on using the matrix $l_1$-norm, more complex nonconvex surrogates are involved, those surrogates being minimized via special numerical procedures. Effectiveness of the approximations is compared via numerical experiment.

Keywords: sparse control, $l_1$-optimization, linear systems, optimal control, linear matrix inequalities.

Funding Agency Grant Number
Russian Science Foundation 16-11-10015


Full text: PDF file (495 kB)
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UDC: 517.977.1
BBK: 22.18
Received: April 17, 2017
Published: July 31, 2017

Citation: A. Bykov, P. S. Shcherbakov, “Numerical study on effectiveness of surrogates for the matrix $l_0$-quasinorm applied to sparse feedback design”, UBS, 68 (2017), 47–73

Citation in format AMSBIB
\Bibitem{BykShc17}
\by A.~Bykov, P.~S.~Shcherbakov
\paper Numerical study on effectiveness of surrogates for the matrix $l_0$-quasinorm applied to sparse feedback design
\jour UBS
\yr 2017
\vol 68
\pages 47--73
\mathnet{http://mi.mathnet.ru/ubs922}
\elib{http://elibrary.ru/item.asp?id=29865000}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Bykov, P. S. Shcherbakov, “Sparse feedback design in discrete-time linear systems”, Autom. Remote Control, 79:7 (2018), 1175–1190  mathnet  crossref  isi  elib
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