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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 10, Pages 1744–1757 (Mi zvmmf394)  

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

Real-time calculation of current optimal feedbacks for a delay system

R. Gabasova, F. M. Kirillovab, O. P. Yarmosha

a Belarussian State University, pr. Nezavisimosti 4, Minsk, 220080, Belarus
b Institute of Mathematics, Belarussian Academy of Sciences, ul. Surganova 11, Minsk, 220072, Belarus

Abstract: A linear optimal control problem for a nonstationary system with a single delay state variable is examined. A fast implementation of the dual method is proposed in which a key role is played by a quasi-reduction of the fundamental matrices of solutions to the homogeneous part of the delay models under analysis. As a result, an iteration step of the dual method involves only the integration of auxiliary systems of ordinary differential equations over short time intervals. A real-time algorithm is described for calculating optimal feedback controls. The results are illustrated by the optimal control problem for a second-order stationary system with a fixed delay.

Key words: delay control systems, quasi-reduction of the fundamental matrix of solutions, fast implementation of the dual method, real-time optimal control.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:10, 1660–1673

Bibliographic databases:

Document Type: Article
UDC: 519.626.2
Received: 05.10.2005
Revised: 02.05.2006

Citation: R. Gabasov, F. M. Kirillova, O. P. Yarmosh, “Real-time calculation of current optimal feedbacks for a delay system”, Zh. Vychisl. Mat. Mat. Fiz., 46:10 (2006), 1744–1757; Comput. Math. Math. Phys., 46:10 (2006), 1660–1673

Citation in format AMSBIB
\Bibitem{GabKirYar06}
\by R.~Gabasov, F.~M.~Kirillova, O.~P.~Yarmosh
\paper Real-time calculation of current optimal feedbacks for a~delay system
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 10
\pages 1744--1757
\mathnet{http://mi.mathnet.ru/zvmmf394}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2304032}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 10
\pages 1660--1673
\crossref{https://doi.org/10.1134/S0965542506100046}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33750360859}


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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. Gabasov R., Kirillova F.M., Pavlenok N.S., “Optimal Control of a Dynamic System Using Perfect Measurements of its States”, Dokl. Math., 85:3 (2012), 436–440  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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