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In this paper, an adaptive wavelet neural network tracking controller is studied for solving control and stability problem of a class of uncertain nonlinear systems. The considered systems in this paper are of the discrete-time form in pure-feedback structure and include the backlash and external disturbance. The backlash nonlinearity input appears non-symmetric in the systems. These systems are more general than those in the previous work. There are major difficulties for stabilizing such systems and in order to overcome the difficulties, by using prediction function of future states, the systems are transformed into an n-step-ahead predictor. The wavelet neural networks are used to approximate the unknown functions and unknown backlash in the transformed systems and the adaption laws are to update neural weights and to compensate for the unknown parameter of backlash. Based on the Lyapunov theory, it is shown that the proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking error converges to a small neighborhood of zero. The simulation of a Single-link robot arm system is provided to verify the effectiveness of the control approach in the paper. Finally, in order to validate, the results of the proposed method are compared with the results of PID and sliding mode controller.

Keywords: Adaptive Tracking control, Wavelet Neural Network, Backlash Nonlinear input, Nonlinear Discrete-time systems, Single Link Robot

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