Optimal control systems by time-dependent coefficients using CAS wavelets
type: Item
instance of: scholarly article
title: Optimal control systems by time-dependent coefficients using CAS wavelets
zbMATH Open document ID: 1185.49033
DOI: 10.1155/2009/636271
author: Taher Abualrub
author: Ibrahim Sadek
author: Marwan Abukhaled
published in: Journal of Applied Mathematics
publication date: 2010-04-14T00:00:00Z
full work available at URL: https://eudml.org/doc/223814
review text: Summary: This paper considers the problem of controlling the solution of an initial boundary-value problem for a wave equation with time-dependent sound speed. The control problem is to determine the optimal sound speed function which damps the vibration of the system by minimizing a given energy performance measure. The minimization of the energy performance measure over sound speed is subjected to the equation of motion of the system with imposed initial and boundary conditions. Using the modal space technique, the optimal control of distributed parameter systems is simplified into the optimal control of bilinear time-invariant lumped-parameter systems. A wavelet-based method for evaluating the modal optimal control and trajectory of the bilinear system is proposed. The method employs finite CAS wavelets to approximate modal control and state variables. Numerical examples are presented to demonstrate the effectiveness of the method in reducing the energy of the system.
Mathematics Subject Classification ID: 49M30
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5692900
zbMATH Keywords: initial boundary-value problem for a wave equation
zbMATH Keywords: minimization of the energy performance measure
zbMATH Keywords: modal space technique
zbMATH Keywords: wavelet-based method
MaRDI profile type: Publication
OpenAlex ID: W1980235876
Wikidata QID: Q58648643
cites work: Q4258421
cites work: Q4423253
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description: scientific article; zbMATH DE number 5692900