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 Izv. IMI UdGU, 2021, Volume 57, Pages 181–189 (Mi iimi416)

MATHEMATICS

On problem of controlling the process of cleaning a pond from impurity

V. I. Ukhobotov, I. V. Izmest'ev

Chelyabinsk State University, ul. Brat'ev Kashirinykh, 129, Chelyabinsk, 454001, Russia

Abstract: The problem of controlling the process of cleaning a pond from impurity using the river flowing from it is considered. A controlled variable is the concentration of impurity entering the river from the pond. The spread of impurity in the river is described by the convection-diffusion equation. This equation includes a term that is determined by other sources of impurity entering the river. The exact value of this term is unknown. Only the boundaries of its change are set. An indicator of the control quality is the value of the linear combination of the concentration of the impurity in the river at a given moment of time and the remaining amount of the mass of the impurity at that moment in the pond. The goal of the control is to bring the value of this indicator within the specified interval.

Keywords: control, uncertainty, convection-diffusion equation.

 Funding Agency Grant Number Russian Foundation for Basic Research 20-41-740027 The research was funded by Russian Foundation for Basic Research and Chelyabinsk Region, project number 20-41-740027.

DOI: https://doi.org/10.35634/2226-3594-2021-57-09

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Bibliographic databases:

UDC: 517.977
MSC: 49N70, 49N75, 91A23, 91A24

Citation: V. I. Ukhobotov, I. V. Izmest'ev, “On problem of controlling the process of cleaning a pond from impurity”, Izv. IMI UdGU, 57 (2021), 181–189

Citation in format AMSBIB
\Bibitem{UkhIzm21} \by V.~I.~Ukhobotov, I.~V.~Izmest'ev \paper On problem of controlling the process of cleaning a pond from impurity \jour Izv. IMI UdGU \yr 2021 \vol 57 \pages 181--189 \mathnet{http://mi.mathnet.ru/iimi416} \crossref{https://doi.org/10.35634/2226-3594-2021-57-09}