Skip to main content
SpringerLink
Log in

Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications

  • Technical Notes and Correspondence
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

A direct adaptive fuzzy control algorithm is developed for a class of uncertain SISO nonlinear systems. In this algorithm, it doesn’t require to assume that the system states are measurable. Therefore, it is needed to design an observer to estimate the system states. Compared with the numerous alternative approaches with respect to the observer design, the main advantage of the developed algorithm is that on-line computation burden is alleviated. It is proven that the developed algorithm can guarantee that all the signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to a small neighborhood around zero. The simulation examples validate the feasibility of the developed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Z. P. Jiang, “Advanced feedback control of the chaotic Duffing equation,” IEEE Trans. on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, no. 2, pp. 244–249, 2002.

    Article  Google Scholar 

  2. C. C. Hua and X. P. Guan, “Adaptive control for chaotic systems,” Chaos, Solitons & Fractals, vol. 22, no. 1, pp. 55–60, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  3. D. Huang, “Adaptive feedback control algorithm,” Physical Review E, vol. 73, 066204, 2006.

  4. C. C. Hua, X. P. Guan, and P. Shi, “Adaptive feedback control for a class of chaotic systems,” Chaos, Solitons & Fractals, vol. 23, no. 3, pp. 757–765, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  5. Y. S. Liu and X. Y. Li, “Decentralized robust adaptive control of nonlinear systems with unmodeled dynamics,” IEEE Trans. on Automatic Control, vol. 47,no. 5, pp. 848–856, 2002.

    Article  Google Scholar 

  6. L. X. Wang, “Fuzzy systems are universal approximators,” Proc. of IEEE International Conference on Fuzzy Systems, San Diego, 1992: 1163–1170.

  7. L. X. Wang, “Stable adaptive fuzzy control of nonlinear systems,” IEEE Trans. on Fuzzy Systems, vol. 1, no. 2, pp. 146–155, 1993.

    Article  Google Scholar 

  8. B. S. Chen, C. H. Lee, and Y. C. Chang, “H∞ tracking design of uncertain nonlinear SISO systems adaptive fuzzy approach,” IEEE Trans. on Fuzzy Systems, vol. 4, no. 1, pp. 32–43, 1996.

    Article  Google Scholar 

  9. J. H. Park, S. J. Seo, and G. T. Park, “Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors,” Fuzzy Sets and Systems, vol. 133, no. 1, pp. 19–36, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  10. N. Essounbouli and A. Hamzaoui, “Direct and indirect robust adaptive fuzzy controllers for a class of nonlinear systems,” International Journal of Control, Automation, and Systems, vol. 4, no. 2, pp. 146–154, 2006.

    Google Scholar 

  11. P. A. Phan and T. J. Gale, “Direct adaptive fuzzy control with less restrictions on the control gain,” International Journal of Control, Automation, and Systems, vol. 5, no. 6, pp. 621–629, 2007.

    Google Scholar 

  12. B. Chen, X. P. Liu, and S. C. Tong, “Adaptive fuzzy approach to control unified chaotic systems,” Chaos, Solitons & Fractals, vol. 34, no. 4, pp. 1180–1187, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  13. G. Besancon, J. Deleon-Morales, and O. Huertaguevara, “On adaptive observers for state affine systems,” International Journal of Control, vol. 79, no. 6, 2006, 581–591.

    Article  MATH  MathSciNet  Google Scholar 

  14. Q. Zhang and B. Delyon, “A new approach to adaptive observer design for MIMO systems,” Proc. of American Control Conference, pp. 1545–1550, 2001.

  15. Q. Zhang, “Revisiting different adaptive observers through a unified formulation,” Proc. of IEEE Conference on Decision and Control, pp. 3067–3072, 2005.

  16. Y. G. Leu, T. T. Lee, and W. Y. Wang, “Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems,” IEEE Trans. Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 29, no.5, pp. 583–591, 1999.

    Article  Google Scholar 

  17. C. H. Wang, T. C. Lin, T. T. Lee, and H. L. Liu, “Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems,” IEEE Trans. on Systems, Man and Cybernetics-Part B: Cybernetics, vol. 32, no. 5, pp. 583–597, 2002.

    Article  Google Scholar 

  18. W. Y. Wang, Y. G. Leu, and T. T. Lee, “Output-feedback control of nonlinear systems using direct adaptive fuzzy-neural controller,” Fuzzy Sets and Systems, vol. 140, no. 2, pp. 341–358, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  19. S. C. Tong and H. X. Li, “Direct adaptive fuzzy output tracking control of nonlinear systems,” Fuzzy Sets and Systems, vol. 128, no. 1, pp. 107–115, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  20. S. C. Tong, H. X. Li, and W. Wang, “Observerbased adaptive fuzzy control for SISO nonlinear systems,” Fuzzy Sets and Systems, vol. 148, no. 3, pp. 355–376, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  21. T. C. Lin, C. H. Wang, and H. L. Liu, “Observer-based indirect adaptive fuzzy-neural tracking control for nonlinear SISO systems using VSS and H∞ approaches,” Fuzzy Sets and Systems, vol. 143, no. 2, pp. 211–232, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  22. X. J. Wei and Y. W. Jing, “Robust adaptive fuzzy controller for nonlinear systems based on approximation errors,” Proc. of American Control Conference, Boston, Massachusetts, pp. 459–463, 2004.

  23. C. C. Kung and T. H. Chen, “Observer-based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems,” Fuzzy Sets and Systems, vol. 155, no. 2, pp. 292–308, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  24. A. Boulkroune, M. Tadjine, M. M’saad, and M. Farza, “How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems,” Fuzzy Sets and Systems, vol. 159, no. 8, pp. 926–948, 2008.

    Article  MathSciNet  Google Scholar 

  25. C. T. Chen, Linear System Theory and Design, 3rd ed., Oxford Univ. Press, London, U.K. 1999.

    Google Scholar 

  26. H. Olsson, K. J. Astrom, C. Canudas, M. Gafvert, and P. Lischinsky, “Friction models and friction compensation,” European Journal of Control, vol. 4 pp. 176–195, 1998.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Physics, Liaoning University of Technology, Jinzhou, Liaoning, 121001, P. R. China

    Yan-Jun Liu, Shao-Cheng Tong & Yong-Ming Li

  2. Research Center of Information and Control, Dalian University of Technology, Dalian, Liaoning, 116023, P. R. China

    Wei Wang

Authors
  1. Yan-Jun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shao-Cheng Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yong-Ming Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan-Jun Liu.

Additional information

Recommended by Editorial Board member Zhong Li under the direction of Editor Young-Hoon Joo. This work is supported by National Natural Science Foundation of China under grant 60674056, 60874056, and the Foundation of Educational Department of Liaoning Province (2008312).

Yan-Jun Liu received the B.S. degree in Applied Mathematics from Shenyang University of Technology in 2001. He received the M.S. degree in Control Theory and Control Engineering from Shenyang University of Technology in 2004 and the Ph.D. degree in Control Theory and Control Engineering from Dalian University of Technology, China, in 2007. His research interests include fuzzy control theory, nonlinear control and adaptive control.

Shao-Cheng Tong received the B.S. degree in Department of Mathematics from Jinzhou Normal College, China, in 1982. He received the M.S. degree in Department of Mathematics from Dalian Marine University in 1988 and the Ph.D. degree in Control Theory and Control Engineering from Northeastern University, China, in 1997. His research interests include fuzzy control theory, nonlinear control, adaptive control, and system identification etc.

Wei Wang received the B.S. degree in Department of Automation from Northeastern University, China, in 1982. He received the M. S. degree in Department of Automation from Northeastern University in 1984 and the Ph.D. degree in Department of Automation from Northeastern University, China, in 1988. His research interests include adaptive predictive control, intelligent control, and production scheduling method etc.

Yong-Ming Li received the B.S. degree in Applied Mathematics from Liaoning University of Technology in 2004. He received the M.S. degree in Applied Mathematics from Liaoning University of Technology in 2007. His research interests include fuzzy control theory, nonlinear control and adaptive control.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, YJ., Tong, SC., Wang, W. et al. Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications. Int. J. Control Autom. Syst. 7, 681–690 (2009). https://doi.org/10.1007/s12555-009-0420-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-009-0420-4

Keywords

Search

Navigation