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Optimal Boundary Control of String Vibrations With Multipoint Intermediate Conditions at Minimizing the Boundary Energy Integral
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Author(s): Vanya Barseghyan (Institute of Mechanics, The National Academy of Sciences of the RA, Yerevan State University, Armenia)and Svetlana Solodusha (Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Russia)
Copyright: 2025
Pages: 22
Source title:
Harnessing AI for Control Engineering
Source Author(s)/Editor(s): Mohamed Arezki Mellal (M'Hamed Bougara University, Algeria)
DOI: 10.4018/979-8-3693-7812-0.ch012
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Abstract
For the equation of string vibration with given initial and final conditions, we consider the problems of optimal boundary control with given multipoint conditions at different intermediate time points for the values of deflection functions and velocities of string points. The control is carried out both by displacement at one end with the other end fixed, and by displacement at the two ends of the string. The minimizable functionals are the boundary energy integrals given over the entire time interval. We propose a constructive approach to designing solutions to the considered problems of optimal boundary control of string vibrations. The construction scheme is as follows: the problems are reduced to control problems with distributed impacts and zero boundary conditions, then, using the method of separation of variables, the obtained problems are reduced to optimal control problems for ordinary differential equations with specified initial, final and multipoint intermediate conditions with appropriate quality criteria.
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