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Robust adaptive fuzzy neural tracking control for a class of unknown chaotic systems

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Abstract

In this paper, an adaptive fuzzy neural controller (AFNC) for a class of unknown chaotic systems is proposed. The proposed AFNC is comprised of a fuzzy neural controller and a robust controller. The fuzzy neural controller including a fuzzy neural network identifier (FNNI) is the principal controller. The FNNI is used for online estimation of the controlled system dynamics by tuning the parameters of fuzzy neural network (FNN). The Gaussian function, a specific example of radial basis function, is adopted here as a membership function. So, the tuning parameters include the weighting factors in the consequent part and the means and variances of the Gaussian membership functions in the antecedent part of fuzzy implications. To tune the parameters online, the back-propagation (BP) algorithm is developed. The robust controller is used to guarantee the stability and to control the performance of the closed-loop adaptive system, which is achieved always. Finally, simulation results show that the AFNC can achieve favourable tracking performances.

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References

  1. G Chen and X Yu (Eds), Chaos control: Theory and applications (Springer-Verlag, Heidelberg, 2003)

    MATH  Google Scholar 

  2. G Chen and J Lü, Dynamics of the Lorenz system family: Analysis, control, and synchronization (Science Press, Beijing, 2003)

    Google Scholar 

  3. E Ott, C Grebogi and J A Yorke, Phys. Rev. Lett. 64, 1196 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. G Chen and X Dong, From chaos to order: Methodologies, perspectives and applications (World Scientific, Singapore, 1998)

    Book  MATH  Google Scholar 

  5. G Chen and X Dong, IEEE Trans. Circuits Syst. I 40, 591 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  6. P Mitra, IEEE Trans. Circuits Syst. I 47, 1649 (2000)

    Article  Google Scholar 

  7. G Chen and X Yu, IEEE Trans. Circuits Syst. I 46, 767 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. X Guan, C Chen, Z Fan and H Peng, Int. J. Bifurcat. Chaos 13, 193 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. K Keiji, H Michio and K Hideki, Phys. Lett. A245, 511 (1998)

    ADS  Google Scholar 

  10. M Jang, C L Chen and C K Chen, Int. J. Bifurcat. Chaos 12, 1437 (2002)

    Article  Google Scholar 

  11. C Fuh and P Tung, Phys. Lett. A218, 240 (1996)

    ADS  Google Scholar 

  12. X Yu, Chaos, Solitons and Fractals 8, 1577 (1997)

    Article  ADS  Google Scholar 

  13. Y Yu and S Zhang, Chaos, Solitons and Fractals 15, 897 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. M Bernardo, Phys. Lett. A214, 139 (1996)

    ADS  Google Scholar 

  15. M Feki, Chaos, Solitons and Fractals 15, 883 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Y J Cao, Phys. Lett. A270, 171 (2000)

    ADS  Google Scholar 

  17. X Wang and M Wang, Int. J. Mod. Phys. B22, 4069 (2008)

    ADS  Google Scholar 

  18. B Chen, X Liu and S Tong, Chaos, Solitons and Fractals 34, 1180 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. J H Kim, C H Hyun, E Kim and M Park, IEEE Trans. Fuzzy Syst. 15, 359 (2007)

    Article  Google Scholar 

  20. H G Zhang, M Li, J Yang and D D Yang, IEEE Trans. Syst. Man Cybern. A39, 437 (2009)

    Google Scholar 

  21. X Wang and J Meng, Chaos 18, 033102 (2008)

    Article  MathSciNet  Google Scholar 

  22. M Roopaei, M Z Jahromi and S Jafari, Chaos 19, 013125 (2009)

    Article  ADS  Google Scholar 

  23. H-T Yau and C-S Shieh, Nonlinear Anal.-Real World Appl. 9, 1800 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  24. Y Gao and M J Er, IEEE Trans. Fuzzy Syst. 11, 462 (2003)

    Article  Google Scholar 

  25. Y Gao and M J Er, IEEE Trans. Neural Netw. 16, 475 (2005)

    Article  Google Scholar 

  26. Y J Liu, W Wang, S C Tong and Y S Liu, IEEE Trans. Syst. Man Cybern. A40, 170 (2010)

    Google Scholar 

  27. Y J Liu and Y Q Zheng, Nonlinear Dyn. 57, 431 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. D Lin and X Wang, Fuzzy Sets Syst. 161, 2066 (2010)

    Article  MATH  Google Scholar 

  29. M Jamshidi, N Vadiee and T J Ress, Fuzzy logic and control (Prentice-Hall, Englewood Cliffs, NJ, 1993)

    Google Scholar 

  30. L X Wang, Adaptive fuzzy systems and control: Design and stability analysis (Prentice-Hall, Englewood Cliffs, NJ, 1994)

    Google Scholar 

  31. Y G Leu, T T Lee and W Y Wang, IEEE Trans. Syst. Man Cybern. B27, 1034 (1997)

    Google Scholar 

  32. C T Lin and C S G Lee, IEEE Trans. Computer 40, 1320 (1991)

    Article  MathSciNet  Google Scholar 

  33. A Isidori, Nonlinear control systems (Springer-Verlag, New York, 1989)

    MATH  Google Scholar 

  34. J E Slotine and W Li, Applied nonlinear control (Prentice-Hall, Englewood Cliffs, NJ, 1991)

    MATH  Google Scholar 

  35. M Hojati and S Gazor, IEEE Trans. Fuzzy Syst. 10, 198 (2002)

    Article  Google Scholar 

  36. Y C Chen and C C Teng, Fuzzy Sets Syst. 73, 291 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  37. L X Wang, IEEE Trans. Fuzzy Syst. 1, 146 (1993)

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    ABDURAHMAN KADIR & XING-YUAN WANG

  2. School of Computer Science and Engineering, Xinjiang University of Finance and Economics, Urumchi, 830012, China

    ABDURAHMAN KADIR & YU-ZHANG ZHAO

Authors
  1. ABDURAHMAN KADIR
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  2. XING-YUAN WANG
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  3. YU-ZHANG ZHAO
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Correspondence to ABDURAHMAN KADIR.

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KADIR, A., WANG, XY. & ZHAO, YZ. Robust adaptive fuzzy neural tracking control for a class of unknown chaotic systems. Pramana - J Phys 76, 887–900 (2011). https://doi.org/10.1007/s12043-011-0071-x

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  • DOI: https://doi.org/10.1007/s12043-011-0071-x

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