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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 11, Pages 1972–1986 (Mi zvmmf379)  

Real-time calculation of the current state estimates for a class of delay systems

R. Gabasova, F. M. Kirillovab, P. V. Makevicha

a Belarussian State University, pr. Skoriny 4, Minsk, 220080, Belarus
b Institute of Mathematics, Belarussian Academy of Sciences, ul. Surganova 11, Minsk, 220072, Belarus
References:
Abstract: The linear optimal observation problem is examined for one type of nonstationary delay system with an uncertainty in the initial state. A fast implementation of the dual method is proposed for calculating estimates of the initial state. This implementation is based on the quasi-reduction of the fundamental matrix of solutions to the mathematical model of delay systems. It is shown that an iteration step of the dual method only requires that auxiliary systems of ordinary differential equations be integrated on small time intervals. An algorithm is described for the real-time calculation of current state estimates. The results are illustrated by the optimal observation problem for a third-order stationary delay system.
Key words: dynamic delay systems, quasi-reduction of fundamental matrix of solutions, fast implementation of dual method, real-time optimal observation.
Received: 16.01.2006
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 11, Pages 1882–1895
DOI: https://doi.org/10.1134/S0965542506110054
Bibliographic databases:
Document Type: Article
UDC: 519.626.2
Language: Russian
Citation: R. Gabasov, F. M. Kirillova, P. V. Makevich, “Real-time calculation of the current state estimates for a class of delay systems”, Zh. Vychisl. Mat. Mat. Fiz., 46:11 (2006), 1972–1986; Comput. Math. Math. Phys., 46:11 (2006), 1882–1895
Citation in format AMSBIB
\Bibitem{GabKirMak06}
\by R.~Gabasov, F.~M.~Kirillova, P.~V.~Makevich
\paper Real-time calculation of the current state estimates for a class of delay systems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 11
\pages 1972--1986
\mathnet{http://mi.mathnet.ru/zvmmf379}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2304070}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 11
\pages 1882--1895
\crossref{https://doi.org/10.1134/S0965542506110054}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845322313}
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