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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 308, Pages 222–231
DOI: https://doi.org/10.4213/tm4065 (Mi tm4065) 		 
Tracking the Solution of a Linear Parabolic Equation Using Feedback Laws

V. I. Maksimovab

a Ural Federal University named after the First President of Russia B. N. Yeltsin, ul. Mira 19, Yekaterinburg, 620002 Russia
b N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia
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DOI: https://doi.org/10.4213/tm4065
Abstract: We consider the problem of tracking the solution of a parabolic equation with an unknown right-hand side by the solution of a similar parabolic equation. To solve this problem, we propose two noise-resistant algorithms based on the extremal shift method known in guaranteed control theory. The first algorithm pertains to the case of continuous measurement of solutions to the equations, and the second, to the case of discrete measurement.
Keywords: parabolic equations, tracking problem.
Received: July 26, 2019
Revised: July 26, 2019
Accepted: December 16, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 308, Pages 208–217
DOI: https://doi.org/10.1134/S0081543820010162
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: V. I. Maksimov, “Tracking the Solution of a Linear Parabolic Equation Using Feedback Laws”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 308, Steklov Math. Inst. RAS, Moscow, 2020, 222–231; Proc. Steklov Inst. Math., 308 (2020), 208–217
Citation in format AMSBIB
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\paper Tracking the Solution of a Linear Parabolic Equation Using Feedback Laws
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 308
\pages 222--231
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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\pages 208--217
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