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Journal of Computer and Systems Sciences International
Published in: Journal of Computer and Systems Sciences International 3/2020

01-05-2020 | CONTROL IN SYSTEMS WITH DISTRIBUTED PARAMETERS

Suppression of Oscillations of Thin Plate by Bounded Control Acting to the Boundary

Authors: I. V. Romanov, A. S. Shamaev

Published in: Journal of Computer and Systems Sciences International | Issue 3/2020

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Abstract

The problem of the exact bounded control of transverse vibrations of a thin plate is considered. Control actions are applied to the boundary of the plate, which fills a certain bounded domain on the plane. The purpose of the control is to completely stop oscillations in a finite time period.
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Literature
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F. L. Chernousko, “Bounded control in distributed-parameter systems,” J. Appl. Math. Mech. 56, 707–723 (1992).MathSciNetCrossRef
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J. L. Lions, “Exact controllability, stabilization and perturbations for distributed systems,” SIAM Rev. 30, 1–68 (1988).MathSciNetCrossRef
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I. V. Romanov, “Control over plate vibrations by boundary forces,” Mosc. Univ. Math. Bull. 66, 53–59 (2011).CrossRef
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I. Romanov and A. Shamaev, “Exact bounded boundary zero-controllability for the two-dimensional wave equation,” arXiv:1603.01212v3 (2018).
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I. V. Romanov and A. S. Shamaev, “On a boundary controllability problem for a system governed by the two-dimensional wave equation,” J. Comput. Syst. Sci. Int. 58, 105 (2019).CrossRef
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D. L. Russell, “Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions,” SIAM Rev. 20, 639–739 (1978).MathSciNetCrossRef
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Metadata
Title
Suppression of Oscillations of Thin Plate by Bounded Control Acting to the Boundary
Authors
I. V. Romanov
A. S. Shamaev
Publication date
01-05-2020
Publisher
Pleiades Publishing
Published in
Journal of Computer and Systems Sciences International / Issue 3/2020
Print ISSN: 1064-2307
Electronic ISSN: 1555-6530
DOI
https://doi.org/10.1134/S1064230720030144

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