Generalized dynamical fuzzy model for identification and prediction

In this paper, the development of an improved Takagi Sugeno (TS) fuzzy model for identification and chaotic time series prediction of nonlinear dynamical systems is proposed. This model combines the advantages of fuzzy systems and Infinite Impulse Response (IIR) filters, which are autoregressive moving average models, to create internal dynamics with just the control input. The structure of Fuzzy Infinite Impulse Response (FIIR) is presented, and its learning algorithm is described. In the proposed model, the Butterworth analogue prototype filters are estimated using the obtained membership functions. Based on the founding orders of the analogue filters, the IIR filters could be constructed. The IIR filters are introduced to each TS fuzzy rule which produces local dynamics. Gustafson–Kessel (GK) clustering algorithm is used to generate the clusters which will be used to find the number of the IIR parameters for each rule. The hybrid genetic algorithm and simplex method are used to identify the consequence parameters. The stability of the obtained model is studied. To demonstrate the performance of this modeling method, three examples have been chosen. Comparative results between the FIIR model on one hand, and the traditional TS fuzzy model, the neural networks and the neuro-fuzzy network on the other hand. The results show that the proposed method provides promising identification results.