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A Kind of Linearization Method in Fuzzy Control System Modeling

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Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2639))

Abstract

A kind of linearization method in fuzzy control system modeling is proposed, in order to deal with the nonlinear model with variable coefficients. The method can turn a nonlinear model with variable coefficients into a linear model with variable coefficients in the way that the membership functions of the fuzzy sets in fuzzy partitions of the universes are changed from triangle waves into rectangle waves. However, the linearization models are incomplete in their forms because of their lacking some items. For solving this problem, joint approximation by using linear models is introduced. The simulation results show that marginal linearization models are of higher approximation precision than their original nonlinear models.

Supported by the National Natural Science Foundation of China (Grant No. 60174013) and the Research Fund for Doctoral Program of Higher Education (Grant No. 20020027013)

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References

  1. Li, H.X., Wang, J.Y., Miao, Z.H.: Modeling on fuzzy control systems. Science in China, Ser(A) 45 (2002) 1506–1517

    MATH  MathSciNet  Google Scholar 

  2. Li, H.X.: Interpolation mechanism of fuzzy control. Science in China, Ser(E) 41 (1998) 312–320

    MATH  Google Scholar 

  3. Li, H.X.: Adaptive fuzzy controllers based on variable universe. Science in China, Ser(E) 42 (1999) 10–20

    MATH  Google Scholar 

  4. Li, H.X.: Relationship between fuzzy controllers and PID controllers. Science in China, Ser(E) 42 (1999) 215–224

    MATH  Google Scholar 

  5. Li, H.X.: Fuzzy logic systems are equivalent to feedforward neural networks. Science in China, Ser(E) 43 (2000) 42–54

    MATH  Google Scholar 

  6. Li, H.X.: To see the success of fuzzy logic from mathematical essence of fuzzy control. Fuzzy Systems and Mathematics (in Chinese) 9 (1995) 1–14

    Google Scholar 

  7. Wang, G.J.: On the foundation of fuzzy reasoning. Lecture in Fuzzy Mathematics and Computer Science, Omaha: Creighton University 4 (1997) 1–24

    Google Scholar 

  8. Li, H.X., Chen, P., Huang, H.P.: Fuzzy Neural Intelligent Systems. Florida: CRC Press (2001)

    Google Scholar 

  9. Li, H.X., Yen, V.C.: Fuzzy Sets and Fuzzy Decision-Making. Florida: CRC Press (1995)

    MATH  Google Scholar 

  10. Koo, T.J.: Stable model reference adaptive fuzzy control of a class of nonlinear systems. IEEE Transactions on Fuzzy Systems 9 (2001) 624–636

    Article  Google Scholar 

  11. Sun, Z.Q.: Theorem and Technology of Intelligence Control. Beijing: Qinghua Publishing House (1997) 16–123

    Google Scholar 

  12. Zhang, N.Y.: Structure analysis of typical fuzzy controllers. Fuzzy Systems and Mathematics (in Chinese) 11 (1997) 10–21

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Beijing Normal University, Beijing, 100875, China

    Hongxing Li, Jiayin Wang & Zhihong Miao

Authors
  1. Hongxing Li
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  2. Jiayin Wang
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  3. Zhihong Miao
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Editor information

Editors and Affiliations

  1. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, 400065, P.R. China

    Guoyin Wang

  2. Department of Computer Science, Nanchang University, Nanchang, 330029, P.R. China

    Qing Liu

  3. Department of Computer Science, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada

    Yiyu Yao

  4. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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© 2003 Springer-Verlag Berlin Heidelberg

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Li, H., Wang, J., Miao, Z. (2003). A Kind of Linearization Method in Fuzzy Control System Modeling. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2003. Lecture Notes in Computer Science(), vol 2639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39205-X_11

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  • DOI: https://doi.org/10.1007/3-540-39205-X_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14040-5

  • Online ISBN: 978-3-540-39205-7

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