Fuzzy Modeling with Multidimensional Membership Functions:Grey-Box Identification and Control Design

Framework for fuzzy modeling and model-based control design

A novel framework for fuzzy modeling and model-based control design is worked out. The fuzzy model is of the Takagi--Sugeno type with constant consequents. It uses multidimensional 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.

Also described in:
J. Abonyi, R. Babuska, F. Szeifert, Fuzzy modeling with multidimensional membership functions: Gray box identification and control design, IEEE Systems, Man and Cybernetics, Part B, 755-767, Oct, 2001

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