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


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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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I. Romanov

National Research University Higher School of Economics; Trapeznikov Institute of Control Sciences

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Email: romm1@list.ru
俄罗斯联邦, Myasnitskaya ul. 20, Moscow, 101000; Profsoyuznaya ul. 65, Moscow, 117997

A. Shamaev

Ishlinskii Institute for Problems in Mechanics; Faculty of Mechanics and Mathematics

Email: romm1@list.ru
俄罗斯联邦, pr. Vernadskogo 101-1, Moscow, 119526; Moscow, 119991

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