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Vladikavkazskii Matematicheskii Zhurnal, 2022, Volume 24, Number 3, Pages 108–119
DOI: https://doi.org/10.46698/s3949-8806-8270-n
(Mi vmj829)
 

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

Optimal control problem for systems modelled by diffusion-wave equation

S. S. Postnov

V. A. Trapeznikov Institute of Control Sciences of RAS, 65 Profsoyuznaya St., 117997 Moscow, Russia
Full-text PDF (252 kB) Citations (1)
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Abstract: This paper deals with an optimal control problem for a model system defined by a one-dimensional non-homogeneous diffusion-wave equation with a time derivative of fractional-order. In general case we consider both of boundary and distributed controls which are $p$-integrable functions (including $p=\infty$). In this case two types of optimal control problem are posed and analyzed: the problem of control norm minimization at given control time and the problem of time-optimal control at given restriction on control norm. The study is based on the use of an exact solution of the diffusion-wave equation, with the help of which the optimal control problem is reduced to an infinite-dimensional $l$-moment problem. We also consider a finite-dimensional $l$-moment problem obtained in a similar way using an approximate solution of the diffusion-wave equation. Correctness and solvability are analyzed for this problem. Finally, an example of boundary control calculation using a finite-dimensional $l$-moment problem is considered.
Key words: optimal control, Caputo derivative, diffusion-wave equation, $l$-problem of moments.
Received: 29.10.2021
Bibliographic databases:
Document Type: Article
UDC: 517.97
Language: Russian
Citation: S. S. Postnov, “Optimal control problem for systems modelled by diffusion-wave equation”, Vladikavkaz. Mat. Zh., 24:3 (2022), 108–119
Citation in format AMSBIB
\Bibitem{Pos22}
\by S.~S.~Postnov
\paper Optimal control problem for systems modelled by diffusion-wave equation
\jour Vladikavkaz. Mat. Zh.
\yr 2022
\vol 24
\issue 3
\pages 108--119
\mathnet{http://mi.mathnet.ru/vmj829}
\crossref{https://doi.org/10.46698/s3949-8806-8270-n}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4489395}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Владикавказский математический журнал
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    References:18
     
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