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Journal of Applied Mathematics
Volume 2009, Article ID 636271, 10 pages
Research Article

Optimal Control Systems by Time-Dependent Coefficients Using CAS Wavelets

Department of Mathematics, American University of Sharjah, Sharjah, UAE

Received 7 July 2009; Accepted 23 November 2009

Academic Editor: M. A. Petersen

Copyright © 2009 Taher Abualrub et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.