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Keywords = transverse vibrations of a piecewise homogeneous string

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13 pages, 577 KiB  
Article
On the Optimal Control Problem for Vibrations of the Rod/String Consisting of Two Non-Homogeneous Sections with the Condition at an Intermediate Time
by Vanya Barseghyan and Svetlana Solodusha
Mathematics 2022, 10(23), 4444; https://doi.org/10.3390/math10234444 - 24 Nov 2022
Cited by 3 | Viewed by 1432
Abstract
We consider an optimal boundary control problem for a one-dimensional wave equation consisting of two non-homogenous segments with piecewise constant characteristics. The wave equation describes the longitudinal vibrations of a non-homogeneous rod or the transverse vibrations of a non-homogeneous string with given initial, [...] Read more.
We consider an optimal boundary control problem for a one-dimensional wave equation consisting of two non-homogenous segments with piecewise constant characteristics. The wave equation describes the longitudinal vibrations of a non-homogeneous rod or the transverse vibrations of a non-homogeneous string with given initial, intermediate, and final conditions. We assume that wave travel time for each of the sections is the same. The control is carried out by shifting one end with the other end fixed. The quality criterion is set on the entire time interval. A constructive approach to building an optimal boundary control is proposed. The results obtained are illustrated with an analytical example. Full article
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