Powerful and flexible fuzzy algorithm for nonlinear dynamic system identification

A new powerful and flexible fuzzy algorithm for nonlinear dynamic system identification is presented. It is based on the identification of the derivative of the system state, instead of the future system state. The membership functions of the underlying static fuzzy model are two-sided Gaussian functions and the learning algorithm is a hybrid-nested routine based on least-squares, quasi-Newton and simplex optimization methods. Moreover, a simple clustering algorithm based on an additional higher level fuzzy model is proposed. The application to the identification of the Mackey-Glass chaotic time series is presented and compared with previous results in terms of maximum error and nondimensional error index. Finally, the application to a test nonlinear dynamic system is presented to show the capabilities of the clustering algorithm. The obtained results show that the proposed algorithm can find wide application in practical problems, as in nonlinear electronic circuit design.