A Adaptive Control System Based on Self-organizing Wavelet Neural Network with H∞ Tracking Performance Compensator

Wavelet neural network (WNN) has high function approximation capability, because it consists of neurons, each of which has a localized and vibratory waveform, and the center of the waveform and its scaling and spatial extent/reduction are adjustable. Therefore it has outstanding ability to adapt to changes of environments. In the field of control engineering, Neural Network (NN) and Fuzzy Neural Network (FNN) are often used as a tool of nonlinear control system design. However it is seldom seen that WNN is used for control system designs. There may be one of only few cases that WNN is used as controller whose structure is furthermore fixed and it requires off-line learning to design the control system. In such case, it is difficult to react to change in the environment. So, we propose an adaptive wavelet neural network control system based on WNN with an adaptable self-organizing network structure and with H-infinity tracking performance compensator to be robust. In addition, we prove stability of the proposed system by Lyapunov stability analysis. Finally, through inverted pendulum control simulations, we showed the proposed system is superior to other conventional control systems.