Admissible Fuzzy Controller in L2 Space

  • Takashi Mitsuishi
  • Yasunari Shidama
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5027)


This article presents a mathematical framework for studying the existence of optimal feedback control based on IF-THEN fuzzy rules through approximate reasoning, and introduces the notion of an admissible fuzzy controller. The framework consists of two propositions: To guarantee the convergence of optimal solution, a set of fuzzy membership functions (admissible fuzzy controller) which are selected out of L 2 space is convex and compact metrizable for the weak topology. And assuming approximate reasoning to be a functional on the set of membership functions, its continuity is proved. Then, we show the existence of a fuzzy controller which minimize (maximize) the integral performance function of the nonlinear feedback system.


Fuzzy control Functional analysis Feedback systems Optimization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Takashi Mitsuishi
    • 1
  • Yasunari Shidama
    • 2
  1. 1.University of Marketing and Distribution SciencesKobeJapan
  2. 2.Shinshu UniversityNaganoJapan

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