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 Trudy Inst. Mat. i Mekh. UrO RAN, 2021, Volume 27, Number 2, Pages 59–66 (Mi timm1814)

On the reconstruction of an unknown input of a system of differential equations

M. S. Blizorukova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: We study the problem of dynamic reconstruction of an unknown input acting on a system of ordinary differential equations nonlinear in the state variables and linear in the control. We consider the case of the absence of instantaneous constraints; i.e., we assume that the unknown perturbation can be unbounded, being a function summable with the square of the Euclidean norm. Taking this fact into account, we construct an algorithm for solving this problem that is resistant to information interferences and computational errors. The algorithm is based on a combination of constructions from the theory of ill-posed problems with the extremal shift method known in positional differential games. The algorithm is focused on the case of “continuous” measurement of the states of the system.

Keywords: system of differential equations, stable reconstruction.

DOI: https://doi.org/10.21538/0134-4889-2021-27-2-59-66

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Bibliographic databases:

UDC: 517.977
MSC: 34A55, 49N45
Revised: 02.04.2021
Accepted:12.04.2021

Citation: M. S. Blizorukova, “On the reconstruction of an unknown input of a system of differential equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 2, 2021, 59–66

Citation in format AMSBIB
\Bibitem{Bli21} \by M.~S.~Blizorukova \paper On the reconstruction of an unknown input of a system of differential equations \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2021 \vol 27 \issue 2 \pages 59--66 \mathnet{http://mi.mathnet.ru/timm1814} \crossref{https://doi.org/10.21538/0134-4889-2021-27-2-59-66} \elib{https://elibrary.ru/item.asp?id=45771402}