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

Janos Abonyi, Robert Babuška, Ferenc Szeifert

Research output: Contribution to journalArticle

45 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)755-767
Number of pages13
JournalIEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Issue number5
Publication statusPublished - Oct 1 2001


  • A priori knowledge
  • Delaunay triangulation
  • Fuzzy modeling
  • Gray-box identification
  • Inverse control
  • Model-based control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Fuzzy modeling with multivariate membership functions: Gray-box identification and control design'. Together they form a unique fingerprint.

  • Cite this