Skip to main content
SpringerLink
Log in

Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign

  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.

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. M. Kristic, I. Kanellakopoulos, P. V. Kokotovic. Nonlinear and Adaptive Control Design, New York, USA: John Wiley and Sons, 1995.

    Google Scholar 

  2. Z. P. Jiang. A combined backstepping and small-gain approach to adaptive output feedback control. Automatica, vol. 35, no. 6, pp. 1131–1139, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  3. L. X. Wang. Adaptive Fuzzy Systems and Control, New Jersey, USA: Prentice Hall 1994.

    Google Scholar 

  4. W. Y. Wang, Y. G. Leu, 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  MathSciNet  MATH  Google Scholar 

  5. A. Boulkroune, M. Tadjine, M. M’saad, 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  MATH  Google Scholar 

  6. F. Qiao, Q. M. Zhu, A. Winfield, C. Melhuish. Adaptive sliding mode control for MIMO nonlinear systems based on a fuzzy logic scheme. International Journal of Automation and Computing, vol. 1, no. 1, pp. 51–62, 2004.

    Article  Google Scholar 

  7. X. Y. Luo, Z. H. Zhu, X. P. Guan. Adaptive fuzzy dynamic surface control for uncertain nonlinear systems. International Journal of Automation and Computing, vol.6, no. 4, pp. 385–390, 2009.

    Article  Google Scholar 

  8. B. Chen, X. P. Liu, S. C. Tong. Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems. IEEE Transactions on Fuzzy Systems, vol. 15, no. 2, pp. 287–300, 2007.

    Article  Google Scholar 

  9. Y. S. Yang, G. Feng, J. S. Ren. A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, vol. 34, no. 3, pp. 406–420, 2004.

    Article  Google Scholar 

  10. A. M. Zou, Z. G. Hou, M. Tan. Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach. IEEE Transactions on Fuzzy Systems, vol. 16, no. 4, pp. 886–897, 2008.

    Article  Google Scholar 

  11. S. S. Zhou, G. Feng, C. B. Feng. Robust control for a class of uncertain nonlinear systems: Adaptive fuzzy approach based on backstepping. Fuzzy Sets and Systems, vol. 151, no. 1, pp. 1–20, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  12. S. C. Tong, Y. M. Li. Adaptive backstepping output feedback control for SISO nonlinear systems using fuzzy neural networks. International Journal of Automation and Computing, vol. 6, no. 2, pp. 145–153, 2009.

    Article  Google Scholar 

  13. S. C. Tong, X. L. He, H. G. Zhang. A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Transactions on Fuzzy Systems, vol. 17, no. 5, pp. 1059–1069, 2009.

    Article  Google Scholar 

  14. S. C. Tong, N. Sheng. Adaptive fuzzy observer backstepping control for a class of uncertain nonlinear systems with unknown time-delay. International Journal of Automation and Computing, vol. 7, no. 2, pp. 236–246, 2010.

    Article  Google Scholar 

  15. M. S. Mahmoud, N. F. Al-Muthairi. Design of robust controllers for time-delay systems. IEEE Transactions on Automatic Control, vol. 39, no. 5, pp. 995–999, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  16. M. Jankovic. Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems. IEEE Transactions on Automatic Control, vol. 46, no. 7, pp. 1048–1060, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  17. X. H. Jiao, T. L. Shen. Adaptive feedback control of nonlinear time-delay systems: The LaSalle-Razumikhin-based approach. IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1909–1913, 2005.

    Article  MathSciNet  Google Scholar 

  18. C. C. Hua, X. P. Guan, P. Shi. Robust backstepping control for a class of time delayed systems. IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 894–899, 2005.

    Article  MathSciNet  Google Scholar 

  19. C. C. Hua, X. P. Guan, P. Shi. Robust output feedback tracking control for time-delay nonlinear systems using neural network. IEEE Transactions on Neural Networks, vol. 18, no. 2, pp. 495–505, 2007.

    Article  Google Scholar 

  20. M. Wang, B. Chen, K. F. Liu, X. P. Liu, S. Y. Zhang. Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients. Information Sciences, vol. 178, no. 22, pp. 4326–4340, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  21. M. Wang, B. Chen, X. P. Liu, P. Shi. Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems. Fuzzy Sets and Systems, vol. 159, no. 8, pp. 949–967, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  22. B. Chen, X. P. Liu, K. F. Liu, P. Shi, C. Lin. Direct adaptive fuzzy control for nonlinear systems with time-varying delays. Information Sciences, vol. 180, no. 5, pp. 776–792, 2010.

    Article  MATH  Google Scholar 

  23. X. D. Ye. Adaptive nonlinear output-feedback control with unknown high-frequency gain sign. IEEE Transactions on Automatic Control, vol. 46, no. 1, pp. 112–115, 2001.

    Article  MATH  Google Scholar 

  24. S. S. Ge, J. Wang. Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Transactions on Neural Network, vol. 13, no. 6, pp. 1409–1419, 2002.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Basic Mathematics, Liaoning University of Technology, Jinzhou, 121001, PRC

    Chang-Liang Liu, Shao-Cheng Tong & Yong-Ming Li

  2. Department of Automatic Control, Beijing Institute of Technology, Beijing, 100081, PRC

    Yuan-Qing Xia

Authors
  1. Chang-Liang 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. Yong-Ming Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuan-Qing Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shao-Cheng Tong.

Additional information

This work was supported by National Natural Science Foundation of China (No. 61074014), the Outstanding Youth Funds of Liaoning Province (No. 2005219001) and Educational Department of Liaoning Province (No. 2006R29, no. 2007T80).

Chang-Liang Liu graduated with a major in mathematics education and applied mathematics from Shandong Education College, Ji’nan, PRC in 2003. He is currently working toward the M. Sc. degree in control theory and control engineering with Liaoning University of Technology, Jinzhou, PRC.

His research interests include fuzzy control theory and nonlinear adaptive control.

Shao-Cheng Tong graduated from Jinzhou Normal College, PRC in 1982. He received the M. Sc. degree from Dalian Marine University in 1988 and the Ph.D. degree from Northeastern University, PRC in 1997. He is currently a professor in the Department of Basic Mathematics, Liaoning University of Technology, PRC.

His research interests include fuzzy control theory and nonlinear adaptive control.

Yong-Ming Li graduated from Liaoning University of Technology, PRC in 2004. He received the M. Sc. degree from Liaoning University of Technology, PRC in 2007. He is currently a lecturer in the Department of Basic Mathematics, Liaoning University of Technology, PRC.

His research interests include fuzzy control theory, nonlinear adaptive control, and intelligent control.

Yuan-Qing Xia graduated from the Department of Mathematics, Chuzhou University, PRC in 1991. He received the M. Sc. degree from Anhui University, PRC in 1998 and Ph.D. degree from Beijing University of Aeronautics and Astronautics, Beijing, PRC in 2001. He is currently a professor in the Department of Automatic Control, Beijing Institute of Technology, PRC.

His research interests include networked control systems, robust control, active disturbance rejection control, and biomedical signal processing.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, CL., Tong, SC., Li, YM. et al. Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign. Int. J. Autom. Comput. 8, 14–22 (2011). https://doi.org/10.1007/s11633-010-0549-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-010-0549-x

Keywords

Search

Navigation