Limited and Smooth Controls of Oscillations in Systems Given by Differential and Integro-Differential Equations

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Abstract

The paper considers the problem of damping vibrations of a membrane and a plate with the help of forces distributed over their entire area. The proposed method allows us to consider restrictions not only on the absolute value of the control, but also on the absolute value of the derivatives of the functions that specify the control. Sufficient conditions are given for the initial conditions under which the problem of bringing the system to rest in a finite time is solvable, and the time of bringing to rest is estimated.

About the authors

T. N. Bobyleva

Moscow State University of Civil Engineering

Author for correspondence.
Email: tatyana2211@outlook.com
Russia, Moscow

I. M. Gusev

Lomonosov Moscow State University

Author for correspondence.
Email: gusevilya94@yandex.ru
Russia, Moscow

A. S. Shamaev

Ishlinsky Institute for Problems in Mechanics RAS

Author for correspondence.
Email: sham@rambler.ru
Russia, Moscow

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