Wavelet Functions Performances in Intelligent Direct Adaptive Control of Uncertain Nonlinear Systems

In this paper, a comparative study of wavelet functions performances in intelligent direct adaptive control is developed. The main idea is to investigate and compare the tracking accuracy of different wavelet activation functions in intelligent control of uncertain nonlinear systems. The most commonly used wavelet families such as Mexican hat, Morlet and Gaussian wavelet are subject of this study. Lyapunov's direct method is used to prove the stability and to derive the Wavelet Neural Networks (WNNs) parameters adaptation laws. The simulation results are presented to classify the wavelet functions under study.