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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 226, Pages 3–15
DOI: https://doi.org/10.36535/0233-6723-2023-226-3-15 (Mi into1196) 		 
Boundary control of some distributed inhomogeneous oscillatory system with intermediate conditions

V. R. Barseghyana, S. V. Solodushabc

a Institute of Mechanics, National Academy of Sciences of Armenia
b L. A. Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk
c Irkutsk State University
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DOI: https://doi.org/10.36535/0233-6723-2023-226-3-15
Abstract: We consider boundary-control problems for a distributed inhomogeneous oscillatory system described by a one-dimensional wave equation with piecewise constant characteristics. We assume that the propagation times for all homogeneous sections are the same. The control is performed by shifting one end with the other end fixed. The initial, intermediate, and final conditions on the deflection function and the velocities of the points of the system are given. An approach to the analytical construction of the boundary control is proposed. The results obtained are illustrated by a specific example. A computational experiment and a comparative analysis were performed.
Keywords: control of oscillations, boundary control, multipoint intermediate states, separation of variables.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWEU-2021-0006, AAAA-A21-121012090034-3
The work of S. V. Solodusha was performed within the framework of the State task of the Ministry of Science and Higher Education of the Russian Federation (project FWEU-2021-0006, theme AAAA-A21-121012090034-3).
Document Type: Article
UDC: 517.977: 534.112
MSC: 93C95, 70Q05
Language: Russian
Citation: V. R. Barseghyan, S. V. Solodusha, “Boundary control of some distributed inhomogeneous oscillatory system with intermediate conditions”, Differential Equations and Mathematical Physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 226, VINITI, Moscow, 2023, 3–15
Citation in format AMSBIB
\Bibitem{BarSol23}
\by V.~R.~Barseghyan, S.~V.~Solodusha
\paper Boundary control of some distributed inhomogeneous oscillatory system with intermediate conditions
\inbook Differential Equations and Mathematical Physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 226
\pages 3--15
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1196}
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