Robust adaptive backstepping control for a class of nonlinear systems using recurrent wavelet neural network

This paper develops a robust adaptive backstepping control (RABC) algorithm for a class of nonlinear systems using a recurrent wavelet neural network (RWNN). This RABC comprises an RWNN controller and a robust controller. The RWNN controller is the main tracking controller utilized to mimic an ideal backstepping control law; and the parameters of RWNN are tuned on-line by adaptation laws derived from the Lyapunov stability theorem and gradient descent method. The robust controller is employed to suppress the influence of approximation error between the RWNN controller and the ideal backstepping control law, so that robust tracking performance of the system can be achieved. Finally, the proposed control method is applied to resolving the marine course-changing and gyros synchronization control problems. Simulation results verify that the proposed control algorithm can achieve favorable tracking performance of these nonlinear systems. Comparison with a wavelet adaptive backstepping control (WABC) and a robust adaptive backstepping control (RABC) partially tuned with adaptation laws demonstrates that the proposed RABC fully tuned with adaptation laws can achieve better control performance than the other two control methods.