Wavelet asymptotic tracking control for uncertain nonlinear systems

A robust adaptive wavelet neural network control of uncertain nonlinear system is proposed to make the tracking error asymptotically converges to zero. Wavelet neural networks are used to approach the unknown functions. All the parameters of wavelet neural networks are tuned online. Robust terms are used to compensate the approximate errors. As different from usual robust terms, time-varying parameters are introduced in robust terms to guarantee the closed-system tracing error converges to zero. The parameters´ update laws of the robust terms are designed by Lyapunov function. The systematic design procedure for the controller is addressed by using the backstepping technique. It is proved that the tracking error asymptotically converges to zero. The proposed method is validated by simulation.