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Abstract
Based on the multi-resolution analysis and the wavelet transform, a wavelet network is presented for the identification and control of nonlinear systems. In view of the rich theory of the wavelet transform, the wavelet network has many advantages. The training of the wavelet network is done using the standard recursive least square which is suitable for online training usually required for adaptive control. Moreover, the network is constructed in a systematic fashion compared to the multilayer neural network which has no systematic rules in construction. Also, better estimation of the unknown functions can be obtained by adding more wavelet units to the network, and these units do not alter the existing trained units. The theoretical ground of the wavelet network is presented in details. The use of the network in the identification of nonlinear systems is examined using simulation studies. Also, the one step ahead controller and the adaptive inverse controller are designed based on the wavelet network and simulation study is done to verifY the analysis. The presented techniques are used to design an adaptive speed controller for the DC motor to achieve high performance speed control even if the motor model is unknown, the load characteristics are also unknown function of speed and the load torque changes online. Experimental results are presented to show the validity of the proposed techniques.