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2009 Optimal Control Systems by Time-Dependent Coefficients Using CAS Wavelets
Taher Abualrub, Ibrahim Sadek, Marwan Abukhaled
J. Appl. Math. 2009: 1-10 (2009). DOI: 10.1155/2009/636271


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.


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Taher Abualrub. Ibrahim Sadek. Marwan Abukhaled. "Optimal Control Systems by Time-Dependent Coefficients Using CAS Wavelets." J. Appl. Math. 2009 1 - 10, 2009.


Published: 2009
First available in Project Euclid: 2 March 2010

zbMATH: 1185.49033
MathSciNet: MR2578311
Digital Object Identifier: 10.1155/2009/636271

Rights: Copyright © 2009 Hindawi

Vol.2009 • 2009
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