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Identification and Control of Dynamic Systems Based on Least Squares Wavelet Vector Machines

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Advances in Neural Networks - ISNN 2006 (ISNN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3972))

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Abstract

A novel least squares support vector machines based on Mexican hat wavelet kernel is presented in the paper. The wavelet kernel which is admissible support vector kernel is characterized by its local analysis and approximate orthogonality, and we can well obtain estimates for regression by applying a least squares wavelet support vector machines (LS-WSVM). To test the validity of the proposed method, this paper demonstrates that LS-WSVM can be used effectively for the identification and adaptive control of nonlinear dynamical systems. Simulation results reveal that the identification and adaptive control schemes suggested based on LS-WSVM gives considerably better performance and show faster and stable learning in comparison to neural networks or fuzzy logic systems. LS-WSVM provides an attractive approach to study the properties of complex nonlinear system modeling and adaptive control.

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References

  1. Lin, C.T., Lee, C.S.G.: Neural Fuzzy System. Prentice-Hall, New Jersey (1996)

    Google Scholar 

  2. Haykin, S.: Neural Networks: A Comprehensive Foundation, 2nd edn. Prentice-Hall, New Jersey (2001)

    Google Scholar 

  3. Vapnik, V.: The Nature of Statistical Learning Theory, 2nd edn. Springer, Heidelberg (1998)

    Google Scholar 

  4. Burges, C.J.C.: A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining Knowl. Disc 2, 1–43 (1998)

    Google Scholar 

  5. Suykens, J.A.K., Vandewalle, J.: Least Squares Support Vector Machine Classifiers. Neural Processing Letters 9, 293–300 (1999)

    Article  MathSciNet  Google Scholar 

  6. Suykens, J.A.K., Gestel, T.V., Brabanter, J.D., Moor, B.D., Vandewalle, J.: Least Squares Support Vector Machines. World Scientific, Singapore (2002)

    Book  MATH  Google Scholar 

  7. Zhang, Q., Benveniste, A.: Wavelet Networks. IEEE Trans. Neural Networks 3, 889–898 (1992)

    Article  Google Scholar 

  8. Zhang, Q.: Using Wavelet Network in Nonparametric Estimation. IEEE Trans. Neural Networks 8, 227–236 (1997)

    Article  Google Scholar 

  9. Zhang, L., Zhou, W.D., Jiao, L.C.: Wavelet Support Vector Machine. IEEE Trans. Systems, Man, and Cybernetics-Part B: Cybernetics 34, 1–6 (2003)

    Google Scholar 

  10. Smola, A., Scholkopf, B., Muller, K.R.: The Connection between Regularization Operators and Support Vector Kernels. Neural Networks 11, 637–649 (1998)

    Article  Google Scholar 

  11. Mallat, S.: A Wavelet Tour of Signal Processing, 2nd edn. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  12. Narendra, K., Parthasarathy, K.: Identification and Control of Dynamical Systems Using Neural Networks. IEEE Trans. on Neural Networks 1, 4–27 (1990)

    Article  Google Scholar 

  13. Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice Hall, Englewood Cliffs (1994)

    Google Scholar 

  14. Barada, S., Singh, H.: Generating Optimal Adaptive Fuzzy-Neural Models of Dynamical Systems with Applications to Control. IEEE Trans. Systems, Man, and Cybernetics-Part C: Applications and Reviews 28, 371–391 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Jun Li & Jun-Hua Liu

Authors
  1. Jun Li
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  2. Jun-Hua Liu
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Editor information

Editors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  2. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

    Zhang Yi

  3. Department of Electrical Engineering, University of Louisville, 40292, Louisville, KY, U.S.A

    Jacek M. Zurada

  4. Laboratory for Computational Biology, Shanghai Center for Systems Biomedicine, 800 Dong Chuan Rd., 200240, Shanghai, China

    Bao-Liang Lu

  5. School of Electrical and Electronic Engineering, University of Manchester, UK

    Hujun Yin

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© 2006 Springer-Verlag Berlin Heidelberg

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Li, J., Liu, JH. (2006). Identification and Control of Dynamic Systems Based on Least Squares Wavelet Vector Machines. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11760023_138

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  • DOI: https://doi.org/10.1007/11760023_138

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34437-7

  • Online ISBN: 978-3-540-34438-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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