Parameter Estimation In Nonlinear Time-Varying Systems Through Takagi-Sugeno Fuzzy Models And Wavelets

In this paper, a parameter estimation problem for a Takagi-Sugeno (TS) fuzzy dynamical system is formulated under the assumption that the premises in the membership functions are known. A linear expression in consequent parameters is obtained under this assumption. If the system is timevarying (TV), the parameters can be determined by recursive estimation techniques. As an alternate approach, the use of multi-resolution wavelets is proposed. Furthermore, a parameter estimation toolbox for fuzzy dynamical models is developed which is then applied to a simple example and to the Mackey-Glass chaotic time series.