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Boundary Control of Some Distributed Heterogeneous Vibrating System with Given States at Intermediate Time Instants

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Abstract

This paper considers the boundary control problem for a distributed heterogeneous vibrating system described by a one-dimensional wave equation with piecewise constant characteristics. The travel time of a wave through each homogeneous section is assumed the same. The control is implemented by displacement at the two ends. A constructive control design approach is proposed to transfer the vibrations on a given time interval from the initial state through the multipoint intermediate states to the terminal state. The control design scheme is as follows: the original problem is reduced to a control problem with distributed actions and zero boundary conditions. Then the variable separation method and control methods for finite-dimensional systems with multipoint intermediate conditions are used. The results are illustrated by an example.

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Authors and Affiliations

  1. Yerevan State University, Yerevan, Armenia

    V. R. Barseghyan

  2. Institute of Mechanics, National Academy of Sciences of the Republic of Armenia, Yerevan, Armenia

    V. R. Barseghyan

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  1. V. R. Barseghyan
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Correspondence to V. R. Barseghyan.

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This paper was recommended for publication by A.G. Kushner, a member of the Editorial Board

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Barseghyan, V.R. Boundary Control of Some Distributed Heterogeneous Vibrating System with Given States at Intermediate Time Instants. Autom Remote Control 84, 117–127 (2023). https://doi.org/10.1134/S0005117923020029

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  • DOI: https://doi.org/10.1134/S0005117923020029

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