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 Avtomat. i Telemekh.: Year: Volume: Issue: Page: Find

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

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: À. Ï. Êóðäþêîâ

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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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
2. S. Srikant, D. Chatterjee, “A jammer's perspective of reachability and LQ optimal control”, Automatica, 70 (2016), 295–302
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
4. A. V. Bykov, P. S. Scherbakov, “Approksimatsii matrichnoi $l_0$-kvazinormy pri sinteze razrezhennykh regulyatorov: chislennye issledovaniya effektivnosti”, UBS, 68 (2017), 47–73
5. K. Kruppa, G. Lichtenberg, “Decentralized state feedback design for multilinear time-invariant systems”, IFAC-PapersOnLine, 50:1 (2017), 5616–5621
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
7. A. Bykov, P. S. Shcherbakov, “Sparse feedback design in discrete-time linear systems”, Autom. Remote Control, 79:7 (2018), 1175–1190
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
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
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
11. Kumar Y., Srikant S., Chatterjee D., “Optimal Multiplexing of Sparse Controllers For Linear Systems”, Automatica, 106 (2019), 134–142
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