New fuzzy wavelet neural networks for system identification and control
By utilizing some of the important properties of wavelets like denoising, compression, multiresolution along with the concepts of fuzzy logic and neural network, new two fuzzy wavelet neural networks (FWNNs) are proposed for approximating any arbitrary non-linear function, hence identifying a non-linear system. The output of discrete wavelet transform (DWT) block, which receives the given inputs, is fuzzified in the proposed two methods: one using compression property and other using multiresolution property. We present a new type of fuzzy neuron model, each non-linear synapse of which is characterized by a set of fuzzy implication rules with singleton weights in their consequents. It is shown that noise and disturbance in the reference signal are reduced with wavelets and also the variation of somatic gain, the parameter that controls the slope of the activation function in the neural network, leads to more accurate output. Identification results are found to be accurate and speed of their convergence is fast. Next, we simulate a control system for maintaining the output at a desired level by using the identified models. Self-learning FNN controller has been designed in this simulation. Simulation results show that the controller is adaptive and robust.
wavelets identification control neuro-fuzzy systems