Continuity of Fuzzy Approximate Reasoning and Its Application to Optimization

  • Takashi Mitsuishi
  • Yasunari Shidama
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4830)


This paper describes a mathematical framework for studying a nonlinear feedback control. The fuzzy control discussed here is the nonlinear feedback control in which the feedback laws are determined by IF-THEN type fuzzy production rules through approximate reasoning introduced by Nakamori. To prove existence of optimal control, we applied compactness of a set of membership functions in L 2 space and continuity of the approximate reasoning, and prepared some propositions concerning approximate reasoning of Nakamori model. By considering fuzzy optimal control problems as problems of finding the minimum (maximum) value of the integral cost (benefit) function on an appropriate set of membership functions, the existence of fuzzy optimal control is shown.


Fuzzy control Nakamori model Optimization Functional analysis 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Takashi Mitsuishi
    • 1
  • Yasunari Shidama
    • 2
  1. 1.University of Marketing and Distribution Sciences, Kobe 651-2188Japan
  2. 2.Shinshu University, Nagano 380-8553Japan

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