This paper proposes a wavelet adaptive backstepping control (WABC) system for a class of second-order nonlinear systems. 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 controller, and the robust controller is designed to achieve L2 tracking performance with desired attenuation level. Since the WNN uses wavelet functions, its learning capability is superior to the conventional 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 performance by incorporating of WNN identification, adaptive backstepping control, and L2 robust control techniques.
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