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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, Volume 30, Number 3, Pages 191–206
DOI: https://doi.org/10.21538/0134-4889-2024-30-3-191-206 (Mi timm2114) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Extremal shift in the problem of tracking a disturbance in a parabolic inclusion describing the two-phase Stefan problem

V. I. Maksimova, Yu. S. Osipovbc

a N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c Lomonosov Moscow State University
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DOI: https://doi.org/10.21538/0134-4889-2024-30-3-191-206
Abstract: The problem of tracking an unknown nonsmooth in time distributed disturbance of a parabolic inclusion describing the two-phase Stefan problem is studied. The problem is reduced to the problem of open-loop control of some appropriately chosen auxiliary system. The control in this system tracks the unknown disturbance in the mean square, and its construction is based on the results of inaccurate measurements of solutions to the given inclusion and to the auxiliary system. Two algorithms for solving the problem that are stable to noise and calculation errors are presented. The algorithms are based on an appropriate modification of Krasovskii's principle of extremal shift known in the theory of guaranteed control.
Keywords: disturbance tracking, parabolic inclusion.
Received: 27.05.2024
Revised: 07.06.2024
Accepted: 10.06.2024
English version:
Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2024, Volume 327, Issue 1, Pages S182–S197
DOI: https://doi.org/10.1134/S0081543824070137
Bibliographic databases:
Document Type: Article
UDC: 517.2, 519.63
MSC: 34A34, 93C20
Language: Russian
Citation: V. I. Maksimov, Yu. S. Osipov, “Extremal shift in the problem of tracking a disturbance in a parabolic inclusion describing the two-phase Stefan problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 30, no. 3, 2024, 191–206; Proc. Steklov Inst. Math., 327, suppl. 1 (2024), S182–S197
Citation in format AMSBIB
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