Operational Matrices of Wavelet and their Applications to Identification in Non-linear Distributed Parameter Systems

The orthogonal function approximation is applied to deal with the identification problem of distributed parameter systems, and Haar wavelets have been chosen as orthogonal functions in this paper. Based on Haar orthogonal wavelets function basis, some operational matrices of Haar wavelet are derived, which are forward integral operational matrix, backward integral operational matrix and element product operational matrix. Moreover, some operational properties of wavelet transformation are obtained. And because these operational matrices and their properties have been applied to the identification problem of distributed parameter systems, an approximation wavelet algorithm has been proposed. Also, the proposed method is more applicable because of consideration of the affect of the initial and boundary conditions. The simulation results have shown the efficiency of the presented algorithm.