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Avtomat. i Telemekh., 2014, Issue 12, Pages 13–27 (Mi at14160)  

This article is cited in 11 scientific papers (total in 11 papers)

Linear Systems

Sparse feedback in linear control systems

B. T. Polyak, M. V. Khlebnikov, P. S. Shcherbakov

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: We consider a classical problem of linear static state feedback design in the linear system $\dot x=Ax+Bu$ subject to a nonstandard constraint that the control vector $u=Kx$ has as many zero components as possible.
A simple approach to approximate solutions of such kind of nonconvex problems is proposed, which is based on convexification. The problem reduces to the minimization of special matrix norms subject to the constraints in the form of linear matrix inequalities (LMIs).
The approach can be generalized to numerous problems of robust and optimal control that admit a “sparse” reformulation. To the best of our knowledge, both the solution and the problem formulation are new.

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English version:
Automation and Remote Control, 2014, 75:12, 2099–2111

Bibliographic databases:

Presented by the member of Editorial Board: . . 

Received: 04.09.2014

Citation: B. T. Polyak, M. V. Khlebnikov, P. S. Shcherbakov, “Sparse feedback in linear control systems”, Avtomat. i Telemekh., 2014, no. 12, 13–27; Autom. Remote Control, 75:12 (2014), 2099–2111

Citation in format AMSBIB
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\by B.~T.~Polyak, M.~V.~Khlebnikov, P.~S.~Shcherbakov
\paper Sparse feedback in linear control systems
\jour Avtomat. i Telemekh.
\yr 2014
\issue 12
\pages 13--27
\mathnet{http://mi.mathnet.ru/at14160}
\transl
\jour Autom. Remote Control
\yr 2014
\vol 75
\issue 12
\pages 2099--2111
\crossref{https://doi.org/10.1134/S0005117914120029}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919338014}


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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. M. V. Khlebnikov, “Control of linear systems subjected to exogenous disturbances: combined feedback”, Autom. Remote Control, 77:7 (2016), 1141–1151  mathnet  crossref  isi  elib  elib
    2. S. Srikant, D. Chatterjee, “A jammer's perspective of reachability and LQ optimal control”, Automatica, 70 (2016), 295–302  crossref  mathscinet  zmath  isi  scopus
    3. Y. Peretz, “On applications of the ray-shooting method for structured and structured-sparse static-output-feedbacks”, Int. J. Syst. Sci., 48:9 (2017), 1902–1913  crossref  mathscinet  zmath  isi
    4. A. V. Bykov, P. S. Scherbakov, “Approksimatsii matrichnoi $l_0$-kvazinormy pri sinteze razrezhennykh regulyatorov: chislennye issledovaniya effektivnosti”, UBS, 68 (2017), 47–73  mathnet  elib
    5. K. Kruppa, G. Lichtenberg, “Decentralized state feedback design for multilinear time-invariant systems”, IFAC-PapersOnLine, 50:1 (2017), 5616–5621  crossref  isi  scopus
    6. Ch. V. Rao, “Sparsity of linear discrete-time optimal control problems with $l_1$ objectives”, IEEE Trans. Autom. Control, 63:2 (2018), 513–517  crossref  mathscinet  zmath  isi  scopus
    7. 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
    8. V. Erofeeva, O. Granichin, O. Granichina, “Multi-sensor task assignment using linear matrix inequalities in the multiple target tracking problem”, IFAC-PapersOnLine, 51:15 (2018), 880–885  crossref  isi  scopus
    9. Y. Kumar, S. Srikant, D. Chatterjee, “On sparse optimal control scheduling for linear systems”, 2018 57th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE, IEEE, 2018, 401–406  crossref  isi
    10. V. Erofeeva, O. Granichin, A. Leonova, “Comparison of multi-sensor task assignment methods: linear matrix inequalities vs. Brute force”, IFAC-PapersOnLine, 51:32 (2018), 648–653  crossref  isi  scopus
    11. Kumar Y., Srikant S., Chatterjee D., “Optimal Multiplexing of Sparse Controllers For Linear Systems”, Automatica, 106 (2019), 134–142  crossref  isi
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