Truncated Chebyshev series approximation of fuzzy systems for control and nonlinear system identification

  • Authors:

  • C. I. Siettos;G. V. Bafas;A. G. Boudouvis

  • Affiliations:

  • Department of Chemical Engineering, National Technical University of Athens, Zografou Campus, Athens 15780, Greece;Department of Chemical Engineering, National Technical University of Athens, Zografou Campus, Athens 15780, Greece;Department of Chemical Engineering, National Technical University of Athens, Zografou Campus, Athens 15780, Greece

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2002

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Abstract

The lack of mathematical models that pertains fuzzy control systems imposes a serious drawback regarding some important tasks such as stability analysis and system identification. For that purpose, the availability of analytical expressions for the fuzzy systems is very important. This paper provides a systematic practical way of approximating fuzzy systems by Chebyshev polynomials, which depend on a finite number of parameters. The proposed methodology is illustrated with two examples: (a) a control problem concerning a tubular reactor which, depending on the operating conditions, may exhibit multiple steady states and (b) the problem of identifying a continuous stirred tank reactor which, at certain values of structural parameters, exhibits stable or unstable steady states or limit cycles.