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Tr. Mat. Inst. Steklova, 2005, Volume 248, Pages 117–123 (Mi tm124)  

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

Optimization of the Boundary Control of an Elastic Force at One Endpoint of a String with the Other Endpoint Fixed

V. A. Il'inab

a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: For a large time interval $T$, we study the boundary control of an elastic force at the endpoint $x=0$ of a string under the condition that the second endpoint $x=l$ of the string is fixed. We determine and present in an analytical form the optimal boundary control $u_x(0,t)=\mu (t)$ that minimizes the elastic boundary energy integral $\int _0^T\mu ^2(t) dt$ over the set of all functions $\mu (t)$ from the class $L_2[0,T]$ under the condition that the oscillation process transfers the string from an arbitrary given initial state into an arbitrary given final state.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 248, 111–117

Bibliographic databases:
UDC: 517.984.5
Received in September 2004

Citation: V. A. Il'in, “Optimization of the Boundary Control of an Elastic Force at One Endpoint of a String with the Other Endpoint Fixed”, Studies on function theory and differential equations, Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 248, Nauka, MAIK Nauka/Inteperiodika, M., 2005, 117–123; Proc. Steklov Inst. Math., 248 (2005), 111–117

Citation in format AMSBIB
\Bibitem{Ili05}
\by V.~A.~Il'in
\paper Optimization of the Boundary Control of an Elastic Force at One Endpoint of a String with the Other Endpoint Fixed
\inbook Studies on function theory and differential equations
\bookinfo Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii
\serial Tr. Mat. Inst. Steklova
\yr 2005
\vol 248
\pages 117--123
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm124}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2165921}
\zmath{https://zbmath.org/?q=an:1116.49313}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 248
\pages 111--117


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    This publication is cited in the following articles:
    1. Hasanov K.K., Gasumov T.M., “Minimal energy control for the wave equation with non-classical boundary condition”, Appl. Comput. Math., 9:1 (2010), 47–56  mathscinet  zmath  isi  elib
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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