1. New Concepts for the Estimation of Takagi-Sugeno Model Based on Extended Kalman Filter

This chapter describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi-Sugeno (TS) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that TS identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the TS method because this type of membership function has been widely used during the last two decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of TS identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of TS fuzzy model. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original TS model. Simulation results indicate the potential, simplicity, and generality of the algorithm. In this chapter we prove that these algorithms converge very fast, thereby making them very practical to use.