Skip to main content
Log in

Output tracking control for generalized high-order nonlinear system with almost disturbance decoupling

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

Abstract

In this paper, we introduce a new method to solve the problem of output tracking control for a class of generalized high-order uncertain nonlinear systems with disturbance. A key contribution of this paper is a result relating its serious uncertainties including unknown high-order terms, unknown nonlinear functions and the signal to be tracked. The main result is that the tracking error belongs to a prescribed small neighborhood of the origin in finite time. Design procedure is presented by improved adding a power integrator method.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Krstić, I. Kanellakopoulos, and P. Kokotović, Nonlinear and Adaptive Control Design, John Wiley and Sons, New York, 1995.

    MATH  Google Scholar 

  2. C. Byrnes, F. Piscoli, and A. Isidori, Nonlinear and Adaptive Control Design, Birkhäuser, Boston, 1997.

    Google Scholar 

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

    MATH  Google Scholar 

  4. I. Karafyllis and Z. Jiang, Stability and Stabilization of Nonlinear Systems, Springer, London, 2011.

    Book  MATH  Google Scholar 

  5. C. Qian and W. Lin, “Practical output tracking of nonlinear systems with uncontrollable unstable linearization,” IEEE Transactions on Automatic Control, vol. 47, no. 1, pp. 21–36, 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  6. W. Lin and R. Pongvuthithum, “Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization,” IEEE Transactions on Automatic Control, vol. 48, no. 10, pp. 1737–1749, 2003. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. X. Yan and Y. Liu, “Global practical tracking by outputfeedback for nonlinear systems with unknown growth rate,” Science China Information Sciences, vol. 54, no. 10, pp. 2079–2090, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  8. Y. Liu and J. Zhang, “Practical output-feedback risksensitive control for stochastic nonlinear systems with stable zero dynamics,” SIAM Journal on Control and Optimization, vol. 45, no. 3, pp. 885–926, 2006. [click]

    Article  MathSciNet  MATH  Google Scholar 

  9. W. Li and J. Zhang, “Distributed practical output tracking of high-order stochastic multi-agent systems with inherent nonlinear drift and diffusion terms,” Automatica, vol. 50, no. 12, pp. 3231–3238, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. A. BenAbdallah, T. Khalifa, and M. Mabrouk, “Adaptive practical output tracking control for a class of uncertain nonlinear systems,” International Journal of Systems Science, vol. 46, no. 8, pp. 1421–1431, 2015. [click]

    MathSciNet  MATH  Google Scholar 

  11. Z. Sun and Y. Liu, “Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems,” Automatica, vol. 43, no. 10, pp. 1772–1783, 2007. [click]

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Qian and W. Lin, “Almost disturbance decoupling for a class of high-order nonlinear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 6, pp. 1208–1214, 2000. [click]

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Chen and W. Zhang, “Guaranteed cost repetitive control for uncertain discrete-time systems,” International Journal of Control, Automation, and Systems, vol. 8, no. 5, pp. 1003–1008, 2010. [click]

    Article  Google Scholar 

  14. X. Jin, Y. He, and Y. He, “Finite-time robust fault-tolerant control against actuator faults and saturations,” IET Control Theory & Applications, vol. 11, no. 4, pp. 550–556, 2017. [click]

    Article  MathSciNet  Google Scholar 

  15. X. Zhang, X. Huang, and H. Lu, “Forwarding-based trajectory tracking control for nonlinear systems with bounded unknown disturbances,” International Journal of Control, Automation, and Systems, vol. 14, no. 5, pp. 1231–1243, 2016. [click]

    Article  Google Scholar 

  16. Z. Sun, C. Zhang, and Z. Wang, “Adaptive disturbance attenuation for generalized high-order uncertain nonlinear systems,” Automatica, vol. 80, no. 6, pp. 102–109, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  17. Z. Sun, T. Li, and S. Yang, “A unified time-varying feedback approach and its applications in adaptive stabilization of high-order uncertain nonlinear systems,” Automatica, vol. 70, no. 8, pp. 249–257, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  18. Z. Sun, L. Xue, and K. Zhang, “A new approach to finitetime adaptive stabilization of high-order uncertain nonlinear system,” Automatica, vol. 58, no. 8, pp. 60–66, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  19. N. Wang, C. Qian, and Z. Sun, “Global asymptotic output tracking of nonlinear second-order systems with power integrators,” Automatica, vol. 80, no. 6, pp. 156–161, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  20. Z. Sun and Y Liu, “Adaptive stabilisation for a large class of high-order uncertain non-linear systems,” International Journal of Control, vol. 82, no. 7, pp. 1275–1287, 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  21. T. Li, Z. Sun, and S. Yang, “Output tracking control for generalized high-order nonlinear system with serious uncertainties,” International Journal of Control, vol. 90, no. 2, pp. 323–333, 2017. [click]

    MathSciNet  Google Scholar 

  22. Z. Sun, Z. Song, and T. Li, “Output feedback stabilization for high-order uncertain feedforward time-delay nonlinear systems,” Journal of the Franklin Institute, vol. 352, no. 11, pp. 5308–5326, 2015.

    Article  MathSciNet  Google Scholar 

  23. Z. Sun, X. Xie, and Z. Liu “Global stabilisation of highorder nonlinear systems with multiple time delays,” International Journal of Control, vol. 86, no. 5, pp. 768–778, 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  24. L. Luo, Y. Wang, and S. Deng, “Adaptive synchronization on uncertain dynamics of high-order nonlinear multi-agent systems with partition of unity approach,” International Journal of Control, Automation, and Systems, vol. 12, no. 2, pp. 259–264, 2014. [click]

    Article  Google Scholar 

  25. Z. Sun and Y. Liu, “Adaptive control design for a class of uncertain high-order nonlinear systems with time delay,” Asian Journal of Control, vol. 17, no. 2, pp. 535–543, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  26. X. Chang and G. Yang, “New results on output feedback H control for linear discrete-time systems,” IEEE Transactions on Automatic Control, vol. 59, no. 5, pp. 1355–1359, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  27. W. Yu, S. Liu, and F. Zhang, “Global output feedback regulation of uncertain nonlinear systems with unknown time delay,” International Journal of Control, Automation, and Systems, vol. 13, no. 2, pp. 327–335, 2015. [click]

    Article  Google Scholar 

  28. H. Wang and Q. Zhu, “Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form,” Automatica, vol. 54, no. 4, pp. 284–291, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  29. Z. Sun, Z. Liu, and X. Zhang, “New results on global stabilization for time-delay nonlinear systems with low-order and high-order growth conditions,” International Journal of Robust and Nonlinear Control, vol. 25, no. 6, pp. 878–899, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Marino and P. Tomei, “Nonlinear output feedback tracking with almost disturbance decoupling,” IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 18–28, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  31. R. Marino and P. Tomei, “Adaptive output feedback regulation with almost disturbance decoupling for nonlinearly parameterized systems,” International Journal of Robust and Nonlinear Control, vol. 10, no. 8, pp. 655–669, 2000. [click]

    Article  MathSciNet  MATH  Google Scholar 

  32. S. Ge and C. Wang, “Adaptive NN control of uncertain nonlinear pure-feedback systems,” Automatica, vol. 38, no. 4, pp. 671–682, 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  33. H. Shen, Y. Zhu, and L. Zhang, “Extended dissipative state estimation for markov jump neural networks with unreliable links,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 2, pp. 346–358, 2017. [click]

    Article  MathSciNet  Google Scholar 

  34. H. Shen, J. Park, Z. Wu, and Z. Zhang, “Finite-time H synchronization for complex networks with semi-Markov jump topology,” Communications in Nonlinear Science and Numerical Simulation, vol. 24, no. 1–3, pp. 40–51, 2015.

    Article  MathSciNet  Google Scholar 

  35. Z. Tang, J. Park, and Z. Zhang, “Dynamic output-feedbackbased H design for networked control systems with multipath packet dropouts,” Applied Mathematics and Computation, vol. 275, no. 2, pp. 121–133, 2016.

    Article  MathSciNet  Google Scholar 

  36. X. Chang, J. Park, and J. Zhou, “Robust static output feedback H control design for linear systems with poly topic uncertainties,” Systems & Control Letters, vol. 85, no. 11, pp. 23–32, 2016.

    Google Scholar 

  37. B. Ren, S. Ge, C. Su, and T. Lee, “Adaptive neural control for a class of uncertain nonlinear systems in pure-feedback form with hysteresis input,” IEEE Transaction on System, Man, and Cybernetics-Part B: Cybernetics, vol. 39, no. 2, pp. 431–443, 2008. [click]

    Google Scholar 

  38. L. Lv, Z. Sun, and X. Xie, “Adaptive control for high-order time-delay uncertain nonlinear system and application to chemical reactor system,” International Journal of Adaptive Control and Signal Processing, vol. 29, no. 2, pp. 224–241, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  39. A. Kurdila, F. Narcowich and J. Ward, “Persistency of excitation in identification using radial basis function approximants,” SIAM Journal on Control and Optimization, vol. 33, no. 2, pp. 625–642, 1995. [click]

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zong-Yao Sun.

Additional information

Recommended by Editor Jessie (Ju H.) Park. This work is supported by Beijing Natural Science Foundation under grant 8164068, National Natural Science Foundation of China under Grant 61773237, Zhejiang Provincial Natural Science Foundation under grant LY16E050003, China Postdoctoral Science Foundation Funded Project under grant 2017M610414, China Earthquake Administration Project of Science for Earthquake Resilience under grants XH16001 and XH17002.

Qing-Quan Tan received his B.S. and M.S. degrees from Qufu Normal University in 2002 and 2005, obtained his Ph.D. degree from Institute of Remote Sensing Applications, Chinese Academy of Sciences, in 2008. He is currently a Senior Engineer in Earthquake Administation of Beijing Municipality, P.R.China. His research interets include analysis and control of nonlinear systems, development and application of information management system.

Ting Li is a master student at the Institute of Automation, Qufu Normal University. Her current research interests include nonlinear control and robust control.

Zong-Yao Sun was born in 1979. He received the M.S. and Ph.D. degrees from Qufu Normal University and Shandong University, China, in 2005 and 2009, respectively. Since 2009 he has been with the Institute of Automation, Qufu Normal University, where he is now an associate Professor. His current research interests include nonlinear control, adaptive control and stability theory of time-delay systems.

Qing-Hua Meng was born in 1977. He received the Ph.D. degree from Zhejiang University, China, in 2005. Since 2005, he has been with the School of Mechanical Engineering, Hangzhou Dianzi Universit, where he is now an Associate Professor. His current research interests include electric vehicle stability control, and Mechanical fault diagnosis and signal processing.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tan, QQ., Li, T., Sun, ZY. et al. Output tracking control for generalized high-order nonlinear system with almost disturbance decoupling. Int. J. Control Autom. Syst. 15, 2570–2578 (2017). https://doi.org/10.1007/s12555-016-0649-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-016-0649-7

Keywords

Navigation