Approximation of feedback linearization control input based on fuzzy wavelet networks



Based on the wavelet transform and fuzzy set theory, we present a fuzzy wavelet network (FWN) for approximating feedback linearization control input. Each fuzzy rule  corresponds to a sub-wavelet neural network (sub-WNN) consisting of wavelets with a specified dilation value. The degree of contribution of each sub-WNN can be controlled flexibly. The constructed  rules  used  to approximate the control signal in which the mathematical model of the system under control is unknown can be adjusted by learning the translation parameters of the selected wavelets and determining the shape of Gaussian membership functions of a fuzzy system. The proposed FWN shows good approximation accuracy and fast convergence. Finally a nonlinear inverted pendulum system is applied to verify the effectiveness and ability of the proposed network.