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

This article is cited in 16 scientific papers (total in 16 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

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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
\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
\jour Autom. Remote Control
\yr 2014
\vol 75
\issue 12
\pages 2099--2111

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    Citing articles on Google Scholar: Russian citations, English citations
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    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. Y. Kumar, S. Srikant, D. Chatterjee, “Optimal multiplexing of sparse controllers for linear systems”, Automatica, 106 (2019), 134–142  crossref  isi
    12. V. Erofeeva, O. Granichin, O. Granichina, A. Sergeenko, S. Trapitsin, “Sensor selection under unknown but bounded disturbances in multi-target tracking problem”, 2019 27Th Mediterranean Conference on Control and Automation (Med), Mediterranean Conference on Control and Automation, IEEE, 2019, 215–220  isi
    13. Ya. Guan, W. X. Zheng, “On design of h-infinity structured controller for decentralized control systems”, 2019 Australian & New Zealand Control Conference (Anzcc), IEEE, 2019, 190–193  crossref  isi
    14. D. S. Solovjev, I. A. Solovjeva, Yu. V. Litovka, V. A. Nesterov, “Searching method for suboptimal action ensuring acceptable losses in the process quality”, J. Mach. Manuf. Reliab., 49:5 (2020), 429–438  crossref  isi
    15. F. Ferrante, F. Dabbene, Ch. Ravazzi, “On the design of structured stabilizers for lti systems”, IEEE Control Syst. Lett., 4:2 (2020), 289–294  crossref  mathscinet  isi
    16. B. T. Polyak, M. V. Khlebnikov, P. S. Shcherbakov, “Linear matrix inequalities in control systems with uncertainty”, Autom. Remote Control, 82:1 (2021), 1–40  mathnet  crossref  crossref  isi
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