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Exact bounded boundary controllability of vibrations of a two-dimensional membrane

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Abstract

The boundary control of vibrations of a plane membrane is considered. A constraint is imposed on the absolute value of the control function. The goal of the control is to drive the membrane to rest. The proof technique used in this paper can be applied to a membrane of any dimension, but the two-dimensional case is considered for simplicity and illustrative purposes.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Myasnitskaya ul. 20, Moscow, 101000, Russia

    I. V. Romanov

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya ul. 65, Moscow, 117997, Russia

    I. V. Romanov

  3. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

    A. S. Shamaev

  4. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. S. Shamaev

Authors
  1. I. V. Romanov
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  2. A. S. Shamaev
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Corresponding author

Correspondence to I. V. Romanov.

Additional information

Original Russian Text © I.V. Romanov, A.S. Shamaev, 2016, published in Doklady Akademii Nauk, 2016, Vol. 470, No. 1, pp. 22–25.

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Romanov, I.V., Shamaev, A.S. Exact bounded boundary controllability of vibrations of a two-dimensional membrane. Dokl. Math. 94, 607–610 (2016). https://doi.org/10.1134/S1064562416050057

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  • DOI: https://doi.org/10.1134/S1064562416050057

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