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 Avtomat. i Telemekh.: Year: Volume: Issue: Page: Find

 Avtomat. i Telemekh., 2007, Issue 2, Pages 127–137 (Mi at945)

Systems with Distributed Parameters

Integral minimization of the second derivative module of the boundary control of string vibrations with the fixed end

A. Yu. Popov

M. V. Lomonosov Moscow State University

Abstract: A problem of boundary control of string vibrations with the fixed end with a bounded control resource is studied. The integral of the second derivative module of the boundary control is minimized. Estimates of upper and lower bounds are found for the extremum. In the vibration suppression problem, at the time period $T$ formulas of boundary control that is close to the optimal control with large values of the time period $T$ are given.

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English version:
Automation and Remote Control, 2007, 68:2, 327–336

Bibliographic databases:

PACS: 02.30.Yy
Presented by the member of Editorial Board: Â. Í. Áóêîâ

Citation: A. Yu. Popov, “Integral minimization of the second derivative module of the boundary control of string vibrations with the fixed end”, Avtomat. i Telemekh., 2007, no. 2, 127–137; Autom. Remote Control, 68:2 (2007), 327–336

Citation in format AMSBIB
\Bibitem{Pop07} \by A.~Yu.~Popov \paper Integral minimization of the second derivative module of the boundary control of string vibrations with the fixed end \jour Avtomat. i Telemekh. \yr 2007 \issue 2 \pages 127--137 \mathnet{http://mi.mathnet.ru/at945} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2301553} \zmath{https://zbmath.org/?q=an:1125.93382} \elib{http://elibrary.ru/item.asp?id=9573493} \transl \jour Autom. Remote Control \yr 2007 \vol 68 \issue 2 \pages 327--336 \crossref{https://doi.org/10.1134/S0005117907020130} \elib{http://elibrary.ru/item.asp?id=13542958} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33947143661}