Fuzzy modeling with multivariate membership functions: gray-box identification and control design

A novel framework for fuzzy modeling and model-based control design is described. The fuzzy model is of the Takagi-Sugeno (TS) type with constant consequents. It uses multivariate antecedent membership functions obtained by Delaunay triangulation of their characteristic points. The number and positi...

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Bibliographic Details
Published inIEEE transactions on systems, man and cybernetics. Part B, Cybernetics Vol. 31; no. 5; pp. 755 - 767
Main Authors Abonyi, J., Babuska, R., Szeifert, F.
Format Journal Article
LanguageEnglish
Published United States IEEE 01.10.2001
Subjects
Algorithms
Control design
Cybernetics
Design engineering
Fuzzy
Fuzzy control
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Fuzzy systems
Input variables
Insertion
Inverse problems
Mathematical models
Parameter estimation
Piecewise linear approximation
Scattering
Space technology
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Summary:A novel framework for fuzzy modeling and model-based control design is described. The fuzzy model is of the Takagi-Sugeno (TS) type with constant consequents. It uses multivariate antecedent membership functions obtained by Delaunay triangulation of their characteristic points. The number and position of these points are determined by an iterative insertion algorithm. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. Finally, methods for control design through linearization and inversion of this model are developed. The proposed techniques are demonstrated by means of two benchmark examples: identification of the well-known Box-Jenkins gas furnace and inverse model-based control of a pH process. The obtained results are compared with results from the literature.
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ISSN:1083-4419
1941-0492
DOI:10.1109/3477.956037