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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.

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ACKNOWLEDGMENTS

The authors dedicate this work to the memory of Prof. L.D. Akulenko, whose work in the field of control theory for systems with distributed parameters significantly influenced the work of the team of the Department of Mechanics of Controlled Systems of the Institute of Mechanics and Mechanics of the Russian Academy of Sciences in this area.

Funding

The work was completed with the financial support of the Russian Science Foundation, project no. 21-11-00151.

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Authors and Affiliations

  1. Moscow State University of Civil Engineering, 129337, Moscow, Russia

    T. N. Bobyleva

  2. Moscow State University, 199991, Moscow, Russia

    I. A. Gusev

  3. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    A. S. Shamaev

Authors
  1. T. N. Bobyleva
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  2. I. A. Gusev
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  3. A. S. Shamaev
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Corresponding authors

Correspondence to T. N. Bobyleva, I. A. Gusev or A. S. Shamaev.

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The authors of this work declare that they have no conflicts of interest.

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In loving memory of L.D. Akulenko

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Bobyleva, T.N., Gusev, I.A. & Shamaev, A.S. Limited and Smooth Controls of Oscillations in Systems Given by Differential and Integro-Differential Equations. Mech. Solids 58, 2818–2825 (2023). https://doi.org/10.3103/S0025654423080058

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  • DOI: https://doi.org/10.3103/S0025654423080058

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