Skip to main content
SpringerLink
Log in

Global output feedback regulation of uncertain nonlinear systems with unknown time delay

  • Regular Papers
  • Control Theory
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper investigates the problem of global output feedback regulation for a class of nonlinear systems with unknown time delay. It is also allowed to contain uncertain functions of all the states and input as long as the uncertainties satisfying certain bounded condition for the considered systems. In this paper, a constructive control technique has been proposed for controlling the systems. By using dynamic high-gain scaling approach and choosing an appropriate Lyapunov-Krasovskii functional, a delay-independent robust adaptive output feedback controller is constructed such that the states of the considered systems achieve global regulation. Two simulation examples are provided to demonstrate the effectiveness of the proposed design scheme.

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. R. Marino and P. Tomei, Nonlinear Control Design, Prentice Hall International, UK, 1995.

    MATH  Google Scholar 

  2. M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.

    Google Scholar 

  3. H. K. Khalil, Nonlinear Systems, 3rd edition, Prentice Hall, New Jersey, 2002.

    MATH  Google Scholar 

  4. L. Praly, “Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate,” IEEE Trans. on Automatic Control, vol. 48, no. 6, pp. 1103–1108, 2003.

    Article  MathSciNet  Google Scholar 

  5. C. J. Qian and W. Lin, “Output feedback control of a class of nonlinear systems: a non-separation principle paradigm,” IEEE Trans. on Automatic Control, vol. 47, no. 7, pp. 1710–1715, 2002.

    Article  MathSciNet  Google Scholar 

  6. P. Krishnamurthy, F. Khorrami, and R. S. Chandra, “Global high gain-based observer and backstepping controller for generalized output-feedback canonical form,” IEEE Trans. on Automatic Control, vol. 48, no. 12, pp. 2277–2284, 2003.

    Article  MathSciNet  Google Scholar 

  7. P. Krishnamurthy and F. Khorrami, “Dynamic highgain scaling: state and output feedback with application to systems with ISS appended dynamics driven by all states,” IEEE Trans. on Automatic Control, vol. 49, no. 12, pp. 2219–2239, 2004.

    Article  MathSciNet  Google Scholar 

  8. H. Lei and W. Lin, “Universal output feedback control of nonlinear systems with unknown growth rate,” Automatica, vol. 42, no. 10, pp. 1783–1789, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Lei and W. Lin, “Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach,” Systems and Control Letters, vol. 56, no. 7–8, pp. 529–537, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. Krishnamurthy and F. Khorrami, “Dual highgain-based adaptive output-feedback control for a class of nonlinear systems,” International Journal of Adaptive Control and Signal Processing, vol. 22, no. 1, pp. 23–42, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  11. F. Shang, Y. G. Liu, and C. H. Zhang, “Adaptive output feedback stabilization for a class of nonlinear systems with inherent nonlinearities and uncertainties,” International Journal of Robust and Nonlinear Control, vol. 21, no. 2, pp. 157–176, 2011.

    Article  MATH  MathSciNet  Google Scholar 

  12. F. Mazenc and S. Bowong, “Tracking trajectories of the cart-pendulum system,” Automatica, vol. 39, no. 4, pp. 677–684, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  13. R. Sepulchre, M. Jankovie, and P. V. Kokotovic, Constructive Nonlinear Control, Springer-Verlag, London, 1997.

    MATH  Google Scholar 

  14. A. R. Teel, “A nonlinear small gain theorem for the analysis of control systems with saturation,” IEEE Trans. on Automatic Control, vol. 41, no. 9, pp. 1256–1270, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  15. P. Krishnamurthy and F. Khorrami, “A high-gain scaling technique for adaptive output feedback control of feedforward systems,” IEEE Trans. on Automatic Control, vol. 49, no. 12, pp. 2286–2292, 2004.

    Article  MathSciNet  Google Scholar 

  16. P. Krishnamurthy and F. Khorrami, “Feedforward systems with ISS appended dynamics: adaptive output-feedback stabilization and disturbance attenuation,” IEEE Trans. on Automatic Control, vol. 53, no. 1, pp. 405–412, 2008.

    Article  MathSciNet  Google Scholar 

  17. H.-L. Choi and J.-T. Lim, “Stabilisation of nonlinear systems with unknown growth rate by adaptive output feedback,” International Journal of Systems Science, vol. 41, no. 6, pp. 673–678, 2010.

    Article  MATH  MathSciNet  Google Scholar 

  18. X. Zhang and Y. Lin, “Global adaptive stabilisation of feedforward systems by smooth output feedback,” IET Control Theory and Applications, vol. 6, no. 13, pp. 2134–2141, 2012.

    Article  MathSciNet  Google Scholar 

  19. J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  21. X. Jiao and T. L. Shen, “Adaptive feedback control of nonlinear time-delay systems: the Lasalle- Razumikhin based Approach,” IEEE Trans. on Automatic Control, vol. 50, no. 11, pp. 1909–1913, 2005.

    Article  MathSciNet  Google Scholar 

  22. X. F. Zhang and Z. L. Cheng, “Global stabilization of a class of time-delay nonlinear systems,” International Journal of Systems Science, vol. 36, no. 8, pp. 461–468, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  23. W. Guan, “Adaptive output feedback control of a class of uncertain nonlinear systems with unknown time delay,” International Journal of Systems Science, vol. 43, no. 4, pp. 682–690, 2012.

    Article  MATH  MathSciNet  Google Scholar 

  24. P. Krishnamurthy and F. Khorrami, “Outputfeedback control of feedforward nonlinear delayed systems through dynamic high-gain scaling,” Proc. of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, pp. 7–12, 2009.

    Google Scholar 

  25. X. F. Zhang, L. Baron, Q. G. Liu, and E.-K. Boukas, “Design of stabilizing controllers with a dynamic gain for feedforward nonlinear time-delay systems,” IEEE Trans. on Automatic Control, vol. 56, no. 3, pp. 692–697, 2011.

    Article  MathSciNet  Google Scholar 

  26. H. K. Khalil and A. Saberi, “Adaptive stabilization of a class of nonlinear systems using high-gain feedback,” IEEE Trans. on Automatic Control, vol. 32, no. 11, pp. 1031–1035, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  27. L. Praly and Z. P. Jiang, “Linear output feedback with dynamic high gain for nonlinear systems,” Systems and Control Letters, vol. 53, no. 2, pp. 107–116, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  28. X. F. Zhang, H. Y. Gao, and C. H. Zhang, “Global asymptotic stabilization of feedforward nonlinear systems with a delay in the input,” International Journal of Systems Science, vol. 37, no. 3, pp. 141–148, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  29. M.-S. Koo, H.-L. Choi, and J.-T. Lim, “Output feedback regulation of a chain of integrators with an unbounded time-varying delay in the input,” IEEE Trans. on Automatic Control, vol. 57, no. 10, pp. 2662–2667, 2012.

    Article  MathSciNet  Google Scholar 

  30. H.-W. Jo, H.-L. Choi and J.-T. Lim, “Measurement feedback control for a class of feedforward nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 23, no. 12, pp. 1405–1418, 2013.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, P. R. China

    Weiyong Yu & Shutang Liu

  2. School of Electrical Engineering and Automation, Qilu University of Technology, Jinan, 250353, P. R. China

    Fangfang Zhang

Authors
  1. Weiyong Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shutang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fangfang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shutang Liu.

Additional information

Weiyong Yu graduated from Jiangxi Normal University, China in 2008. He received his M.S. degree from Guangxi University, China in 2011. He is currently a Ph.D. candidate at Shandong University. His research interests include adaptive control, nonlinear systems and timedelay systems.

Shutang Liu received his Ph.D. degree in Control Theory and Control Engineering from South China University of Technology and City University of Hong Kong, China in 2002. From 2003 to 2005, he was doing postdoctoral research at Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China. Presently, he is a professor and doctoral supervisor at College of Control Science and Engineering, Shandong University, China. His research interests include spatial chaotic theory of nonlinear dynamical systems and its application, qualitative theory and qualitative control of complex system, control and applications of fractals and so on.

Fangfang Zhang received her M.S. degree from Beijing University of Technology, China and her Ph.D. degree from Shandong University, in 2006 and 2014, respectively. She is currently a lecture in the School of Electrical Engineering and Automation, Qilu University of Technology. Her research interests include adaptive control, chaos control and intelligent control.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, W., Liu, S. & Zhang, F. Global output feedback regulation of uncertain nonlinear systems with unknown time delay. Int. J. Control Autom. Syst. 13, 327–335 (2015). https://doi.org/10.1007/s12555-013-0480-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-013-0480-3

Keywords

Search

Navigation