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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 2, Pages 150–159 (Mi timm1177)  
On a modification of the extremal shift method for a second-order differential equation in a Hilbert space

V. I. Maksimovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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Abstract: A problem of tracking a solution of a second-order differential equation in a Hilbert space by a solution of another equation is considered. It is assumed that the first (reference) equation is subject to the action of an unknown control, which is unbounded in time. In the case when the current states of both equation are observed with small errors, a solution algorithm stable with respect to informational noises and computational inaccuracies is designed. The algorithm is based on N.N.Krasovskii's extremal shift method known in the theory of guaranteed control.
Keywords: tracking a solution, extremal shift, second-order equation.
Received: 05.02.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 293, Issue 1, Pages 137–147
DOI: https://doi.org/10.1134/S0081543816050126
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: V. I. Maksimov, “On a modification of the extremal shift method for a second-order differential equation in a Hilbert space”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 150–159; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 137–147
Citation in format AMSBIB
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\paper On a modification of the extremal shift method for a second-order differential equation in a Hilbert space
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\vol 21
\issue 2
\pages 150--159
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 293
\issue , suppl. 1
\pages 137--147
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