Improved polynomial fuzzy modeling and controller with stability analysis for nonlinear dynamical systems
type: Item
instance of: scholarly article
title: Improved polynomial fuzzy modeling and controller with stability analysis for nonlinear dynamical systems
zbMATH Open document ID: 1264.93124
DOI: 10.1155/2012/273631
author: Hamed Kharrati
author: Sohrab Khanmohammadi
author: Witold Pedrycz
author: Ghasem Alizadeh
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We present 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.
Mathematics Subject Classification ID: 93C42
zbMATH DE Number: 6173147
Wikidata QID: Q58911364
describes a project that uses: Sostools
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/273631
OpenAlex ID: W2157193389
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description: scientific article; zbMATH DE number 6173147