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

A novel framework for fuzzy modeling and model-based control design is desc ribed. The fuzzy model is of the Takagi-Sugeno (TS) type with constant cons equents. It uses multivariate antecedent membership functions obtained by D elaunay triangulation of their characteristic points. The number and positi on of these points are determined by an iterative insertion algorithm. Cons trained optimization is used to estimate the consequent parameters, where t he constraints are based on control-relevant a priori knowledge about the m odeled process. Finally, methods for control design through linearization a nd inversion of this model are developed. The proposed techniques are demon strated by means of two benchmark examples: identification of the well-know n Box-Jenkins gas furnace and inverse model-based control of a pH process. The obtained results are compared with results from the literature.