Two new approaches for linguistic fuzzy modeling and introduction to their stability analysis

2003 ◽  
Author(s):  
A.A. Suratgar ◽  
S.K. Nikravesh
Keyword(s):  
Stability Analysis ◽  
Fuzzy Modeling ◽  
New Approaches ◽  
Linguistic Fuzzy Modeling

scholarly journals Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Hamed Kharrati ◽  
Sohrab Khanmohammadi ◽  
Witold Pedrycz ◽  
Ghasem Alizadeh
Keyword(s):  
Stability Analysis ◽  
Nonlinear Dynamical Systems ◽  
Fitness Function ◽  
Fuzzy Model ◽  
Taylor Series Expansion ◽  
Fuzzy Modeling ◽  
Lyapunov Theory ◽  
Membership Functions ◽  
Polynomial Fuzzy Systems ◽  
Nonlinear Plant

This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS) approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.

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