Wavelet adaptive backstepping control for a class of nonlinear systems

Abstract—This paper proposes a wavelet adaptive backstepping control (WABC) system for a class of second-order nonlinear sys-tems. The WABC comprises a neural backstepping controller and a robust controller. The neural backstepping controller containing a wavelet neural network (WNN) identifier is the principal con-troller, and the robust controller is designed to achieveL 2 tracking performance with desired attenuation level. Since the WNN uses wavelet functions, its learning capability is superior to the con-ventional neural network for system identification. Moreover, the adaptation laws of the control system are derived in the sense of Lyapunov function and Barbalat’s lemma, thus the system can be guaranteed to be asymptotically stable. The proposed WABC is applied to two nonlinear systems, a chaotic system and a wing-rock motion system to illustrate its effectiveness. Simulation results verify that the proposed WABC can achieve favorable tracking per-formance by incorporating of WNN identification, adaptive back-stepping control, and L 2 robust control techniques. Index Terms—Adaptive control, backstepping control, chaotic system, robust control, wavelet neural network (WNN), wing-rock system. I