New Concepts for the Estimation of Takagi-Sugeno Model Based on Extended Kalman Filter - Fuzzy Modeling and Control: Theory and Applications - page 2

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

Basil Mohammed Al-Hadithi, Agustín Jiménez, Fernando Matía,
José Manuel Andújar and Antonio Javier Barragán

1.1 Introduction

Nonlinear control systems based on the Takagi-Sugeno (TS) fuzzy model (Takagi
and Sugeno 1985 ) have attracted lots of attention during the last 20years (Chen
et al. 2007 ; Gang 2006 ; Guerra and Vermeiren 2004 ; Hou et al. 2007 ; Hseng et al.
2007 ; Jae-Hun et al. 2007 ; Jiang and Han 2007 ; Lian et al. 2006 ; Tanaka et al.
2003 ), in opposition to nonlinear control systems design methods based on Mam-
dani fuzzy model (Matía et al. 1992 ). It provides a powerful solution for development
of function approximation, systematic techniques to stability analysis and controller
design of fuzzy control systems in view of fruitful conventional control theory and
techniques. They also allow relatively easy application of powerful learning tech-
niques for their identification from data (Cordon et al. 2001 ). This model (Takagi
and Sugeno 1985 ) is formed by using a set of fuzzy rules to represent a nonlinear
systemas a set of local affinemodels which are connected by fuzzymembership func-
tions. The authors divide the identification process in three steps; premise variables,
membership functions and consequent parameters.With respect tomembership func-
tions, they apply nonlinear programming technique using the complex method for
the minimization of the performance index. This fuzzy modeling method presents
an alternative technique to represent complex nonlinear systems (Tanaka and Wang
2001 ) and reduces the number of rules in modeling higher order nonlinear systems
(Gang 2006 ; Takagi and Sugeno 1985 ). TS fuzzy models are proved to be universal
function approximators as they are able to approximate any smooth nonlinear func-
tions to any degree of accuracy in any convex compact region (Johansen et al. 2000 ;