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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 1, Pages 160–169 (Mi timm910)  

This article is cited in 1 scientific paper (total in 1 paper)

Reconstruction of distributed controls in parabolic systems by a dynamic method

A. I. Korotkiiab, D. O. Mikhailovab

a Ural Federal University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (249 kB) Citations (1)
References:
Abstract: We consider the problem of reconstructing a priori unknown distributed controls in parabolic systems from results of approximate measurements of states of the system's observed motion. The problem is solved in the dynamic variant, when a current approximation of the unknown control is found only from the measurements received no later than the current time. The problem under consideration is ill-posed. We propose to solve it by the method of dynamic regularization and construct new dynamic regularization algorithms, which provide a strengthened convergence of regularized approximations, in particular, their piecewise uniform convergence. A finite-dimensional approximation of the problem is carried out and results of numerical simulation are presented.
Keywords: dynamic system, control, reconstruction, observation, measurement, inverse problem, regularization, method of dynamic regularization, variation, piecewise uniform convergence.
Received: 22.10.2012
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. I. Korotkii, D. O. Mikhailova, “Reconstruction of distributed controls in parabolic systems by a dynamic method”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 1, 2013, 160–169
Citation in format AMSBIB
\Bibitem{KorMik13}
\by A.~I.~Korotkii, D.~O.~Mikhailova
\paper Reconstruction of distributed controls in parabolic systems by a~dynamic method
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2013
\vol 19
\issue 1
\pages 160--169
\mathnet{http://mi.mathnet.ru/timm910}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3408371}
\elib{https://elibrary.ru/item.asp?id=18839275}
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  • https://www.mathnet.ru/eng/timm/v19/i1/p160
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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    Abstract page:391
    Full-text PDF :98
    References:64
    First page:10
     
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