Adaptive learning control for finite interval tracking based on variable wavelet neural network

This paper is concerned with the nonlinearly parametric adaptive iterative learning control for unknown nonlinear system. Using a variable wavelet neural network (WNN) to approximate unknown nonlinearities, where the number of basis functions gradually increasing following the iterations, a robust state feedback adaptive control approach is derived in the sense of Lyapunov function. Under a reasonable assumption on variable WNN, which can relax the limitation of fixed neural networks used in traditional approaches, the adaptive laws for nonlinear parameters in variable WNN are proposed for the first time, which can resist the disturbance deduced from the variation of WNN´s structure. With this proposed controller, it is proved that all signals of closed-loop system are bounded over iteration and time domain, and the tracking error converges to a small neighborhood of the origin in the sense of L_2,T norm after a finite number of learning iterations, by choosing appropriate design parameters. Furthermore, the approach can be extended to strict feedback system. Finally, an example and some comparisons are given to demonstrate the effectiveness of the method proposed in this paper.