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Avtomat. i Telemekh., 2006, Issue 10, Pages 20–46 (Mi at1244)  

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

Invariance and polynomial design of strategies in the linear-quadratic game

A. E. Barabanov

Saint-Petersburg State University

Abstract: A new algorithm to solve the $\mathcal H^\infty$ control problem in the case of full information was presented. It combines the spectral and matrix methods. The polynomial Lur'e–Riccati operator was introduced. Parametrization of all solutions of the controlled plant equation by hidden variables was presented within the framework of the J. C. Willems behavioral approach. The kernel of the polynomial Lur'e–Riccati operator was decomposed into the direct sum of subspaces that are similar to the Jordan blocks. The saddle point of the linear-quadratic game which was found by V. A. Yakubovich in 1970 was shown to provide solution to the $\mathcal H^\infty$ control problem for a considerable class of controlled plants.

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English version:
Automation and Remote Control, 2006, 67:10, 1547–1572

Bibliographic databases:

PACS: 02.30.Yy
Presented by the member of Editorial Board: Б. Т. Поляк

Received: 26.01.2006

Citation: A. E. Barabanov, “Invariance and polynomial design of strategies in the linear-quadratic game”, Avtomat. i Telemekh., 2006, no. 10, 20–46; Autom. Remote Control, 67:10 (2006), 1547–1572

Citation in format AMSBIB
\Bibitem{Bar06}
\by A.~E.~Barabanov
\paper Invariance and polynomial design of strategies in the linear-quadratic game
\jour Avtomat. i Telemekh.
\yr 2006
\issue 10
\pages 20--46
\mathnet{http://mi.mathnet.ru/at1244}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2268316}
\zmath{https://zbmath.org/?q=an:1195.49044}
\transl
\jour Autom. Remote Control
\yr 2006
\vol 67
\issue 10
\pages 1547--1572
\crossref{https://doi.org/10.1134/S000511790610002X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33750190554}


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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. E. Barabanov, “Minimax Control for Nonstationary Linear Operator Systems”, Proc. Steklov Inst. Math., 262 (2008), 26–43  mathnet  crossref  mathscinet  zmath  isi  elib  elib
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