Analysis and design of uncertain fuzzy control systems - Part I : Fuzzy modelling and identification

This paper is the first part of two papers dealing with the analysis and design of a class of fuzzy control systems with uncertainty and disturbance. This paper first analyzes the Mamdani and Takagi-Sugeno type fuzzy models which are widely used in the control area and argues that both of these fuzzy models cannot represent the uncertainties of a complex system. A new kind of dynamical fuzzy model called uncertain fuzzy model is proposed to represent a complex system which includes both linguistic information and system uncertainties. A new identification approach is then developed for the uncertain fuzzy model. Contrary to the prevailing LS methods, the final identification results are not parameters of a system model, but a feasible set of parameters which is consistent with the model structure, data and system uncertainties. The identification method is a kind of optimal recursive ellipsoid algorithm which is based on the famous Khachiyan ellipsoid algorithm in the context of linear programming.