Nonlinear Systems

Boundary control of some distributed heterogeneous vibrating system with given states at intermediate time instants

V. R. Barseghyan<sup>ab

a</sup> Yerevan State University, Yerevan, Armenia
^b Institute of Mechanics, National Academy of Sciences of the Republic of Armenia, Yerevan, Armenia

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.

Keywords: vibration control, boundary control, heterogeneous vibrating process, wave equation, piecewise constant characteristics, separation of variables.

Presented by the member of Editorial Board: A. G. Kushner

Received: 08.03.2022
Revised: 15.09.2022
Accepted: 26.10.2022

DOI: 10.31857/S0005231023020046

 English version: Automation and Remote Control, 2023, 84:2, 117–127