On the Optimal Control Problem for Vibrations of the Rod/String Consisting of Two Non-Homogeneous Sections with the Condition at an Intermediate Time

Vanya Barseghyan and Svetlana Solodusha ()
Additional contact information
Vanya Barseghyan: Institute of Mechanics, The National Academy of Sciences of the Republic of Armenia, Yerevan State University, Yerevan 0019, Armenia
Svetlana Solodusha: Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, 664033 Irkutsk, Russia

Mathematics, 2022, vol. 10, issue 23, 1-13

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, 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.

Keywords: optimal vibration control; longitudinal vibrations of a piecewise homogeneous rod; transverse vibrations of a piecewise homogeneous string; optimal boundary control; intermediate condition; separation of variables (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/23/4444/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/23/4444/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:23:p:4444-:d:983470

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().