Recurrent wavelet neural backstepping controller design with a smooth compensator

Recurrent wavelet neural network (RWNN) has the advantages in its dynamic responses and information storing ability. This paper develops a recurrent wavelet neural backstepping control (RWNBC) scheme for multiple-input multiple-output (MIMO) mechanical systems. This proposed RWNBC comprises a neural controller and a smooth compensator. The neural controller using an RWNN is the principal tracking controller utilized to mimic an ideal backstepping control law; and the parameters of RWNN are online tuned by the derived adaptation laws from the Lyapunov stability theorem. The smooth compensator is designed to dispel the approximation error introduced by the neural controller, so that the asymptotic stability of the closed-loop system can be guaranteed. Finally, two MIMO mechanical systems, a mass-spring-damper system and a two-inverted pendulum system, are performed to verify the effectiveness of the proposed RWNBC scheme. From the simulation results, it is verified that the proposed RWNBC scheme can achieve favorable tracking performance without any chattering phenomenon.