Parameter estimation in nonlinear time-varying systems through Takagi-Sugeno fuzzy models and wavelets

Abstract

In this paper, a parameter estimation problem for a Takagi-Sugeno fuzzy dynamic 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 time-varying, 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 dynamic models is developed which is then applied to a simple example and to the Mackey-Glass chaotic time series.