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Continuity of Defuzzification on L2 Space for Optimization of Fuzzy Control

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Book cover Active Media Technology (AMT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7669))

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Abstract

The purpose of this study is to consider the fuzzy optimal control based on the functional analysis. We used a mathematical approach to compute optimal solutions. The feedback of fuzzy control is evaluated through approximate reasoning using the center of sums defuzzification method or the height method on IF-THEN fuzzy rules. 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 continuous function space is compact metrizable. 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 minimizes (maximizes) the integral performance function of the nonlinear feedback fuzzy system.

This work was supported by JSPS KAKENHI Grant Numbers 24700235, 23730395.

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Author information

Authors and Affiliations

  1. University of Marketing and Distribution Sciences, Kobe, Japan

    Takashi Mitsuishi, Nami Shimada & Kiyoshi Sawada

  2. Center for Green Computing, Nagoya Institute of Technology, Nagoya, Japan

    Takanori Terashima

  3. Osaka University of Economics, Osaka, Japan

    Toshimichi Homma

  4. Shinshu University, Nagano, Japan

    Yasunari Shidama

Authors
  1. Takashi Mitsuishi
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  2. Takanori Terashima
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  3. Nami Shimada
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  4. Toshimichi Homma
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  5. Kiyoshi Sawada
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  6. Yasunari Shidama
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Editor information

Editors and Affiliations

  1. Faculty of Computer and Information Sciences, Hosei University, 3-7-2, Kajino-cho, 184-8584, Koganei-shi, Tokyo, Japan

    Runhe Huang

  2. Faculty of Computer Science, University of New Brunswick, Box 440, E3B 5A3, Fredicton, NB, Canada

    Ali A. Ghorbani

  3. Department of Informatics, Systems and Communication, University of Milano Bicocca, Viale Sarca 336, 20126, Milano, Italy

    Gabriella Pasi

  4. Department of Administration Engineering, Keio University, 3-14-1 Hiyoshi, 223-8522, Kohoku-ku, Yokohama, Japan

    Takahira Yamaguchi

  5. University of Aizu, 102-C, Research Quadrangles, Tsuruga, Ikki-machi, 965-8580, Aizu-Wakamatsu City, Fukushima, Japan

    Neil Y. Yen

  6. Institute of Software, Chinese Academy of Sciences, no.4 Nan Sie Jie, Zhong Guan Cun, Hai Dian Qu, 100190, Beijing, China

    Beijing Jin

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© 2012 Springer-Verlag Berlin Heidelberg

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Mitsuishi, T., Terashima, T., Shimada, N., Homma, T., Sawada, K., Shidama, Y. (2012). Continuity of Defuzzification on L2 Space for Optimization of Fuzzy Control. In: Huang, R., Ghorbani, A.A., Pasi, G., Yamaguchi, T., Yen, N.Y., Jin, B. (eds) Active Media Technology. AMT 2012. Lecture Notes in Computer Science, vol 7669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35236-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-35236-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35235-5

  • Online ISBN: 978-3-642-35236-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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