Skip to main content
Log in

Adaptive Event-triggered Control for High-order Nonlinear Systems with Deferred Asymmetric Full-state Constraints

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

Abstract

This paper investigates the adaptive event-triggered tracking problem for high-order nonlinear systems with deferred asymmetric time-varying full-state constraints. Firstly, a shifting function is introduced to remove the constraint bounds of the system state’s initial value, and a novel time-varying nonlinear function is adopted to deal with the asymmetric full-state constraints. Secondly, a coordinate transformation combining dynamic surface technology is proposed to remove the feasibility condition on virtual controllers. Then, an adaptive state-feedback event-triggered controller is designed to guarantee that the closed-loop system is stable and the asymmetric full-state constraints are maintained. Finally, the simulation is provided to illustrate the effectiveness of the control scheme.

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. W. Lin and C. J. Qian, “Adding one power integrator: a tool for global stabilization of high-order lower-biangular systems,” Systems and Control Letters, vol. 39, no. 5, pp. 339–351, April 2000.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. W. Q. Li, X. J. Xie, and S. Y. Zhang, “Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions,” SIAM Journal on Control and Optimization, vol. 49, no. 3, pp. 1262–1282, January 2011.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. C. Chen, C. J. Qian, and X. Z. Lin, “Smooth output feedback stabilization for a class of nonlinear systems with time-varying powers,” International Journal of Robust and Nonlinear Control, vol. 27, no. 18, pp. 5113–5128, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. C. Man and Y. G. Liu, “Global adaptive stabilization and practical tracking for nonlinear systems with unknown powers,” Automatica, vol. 100, pp. 171–181, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  6. C. P. Bechlioulis and G. A. Rovithakis, “Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2090–2099, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Q. Mayne, J. B. Rawlings and C. V. Rao, “Constrained model predictive control: stability and optimality,” Automatica, vol. 36, no. 6, pp. 789–814, June 2000.

    Article  MathSciNet  MATH  Google Scholar 

  8. K. B. Ngo, R. Mahony, and Z. P. Jiang, “Integrator back-stepping using barrier functions for systems with multiple state constraints,” Proc. of the 44th IEEE Conference on Decision and Control, pp. 8306–8312, 2005.

  9. K. Zhao and Y. D. Song, “Removing the feasibility conditions imposed on tracking control designs for state-constrained strict-feedback systems,” IEEE Transactions on Automatic Control, vol. 64, no. 3, pp. 1265–1272, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  10. T. L. Guo, X. Y. Wang, and S. H. Li, “Stabilisation for a class of high-order nonlinear systems with output constraints,” IET Control Theory & Applications, vol. 10, no. 16, pp. 2128–2135, October 2016.

    Article  MathSciNet  Google Scholar 

  11. C. C. Chen, “A unified approach to finite-time stabilization of high-order nonlinear systems with and without an output constraint,” International Journal of Robust and Nonlinear Control, vol. 29, no. 2, pp. 393–407, January 2019.

    Article  MathSciNet  MATH  Google Scholar 

  12. K. W. Li and Y. M. Li, “Adaptive fuzzy finite-time dynamic surface control for high-order nonlinear system with output constraints,” International Journal of Control, Automation, and Systems, vol. 19, no. 1, pp. 112–123, January 2021.

    Article  Google Scholar 

  13. S. Ling, H. Q. Wang, and P. X. Liu, “Adaptive tracking control of high-order nonlinear systems under asymmetric output constraint,” Automatica, vol. 122, 109281, 2020.

    Article  MathSciNet  MATH  Google Scholar 

  14. W. Sun, S. F. Su, G. W. Dong, and W. W. Bai, “Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 3, pp. 1496–1506, 2021.

    Google Scholar 

  15. N. Wang, F. Z. Tao, Z. M. Fu, and S. Z. Song, “Adaptive fuzzy control for a class of stochastic strict feedback high-order nonlinear systems with full-state constraints,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 1, pp. 205–213, January 2022.

    Article  Google Scholar 

  16. C. Guo, R. M. Xie, and X. J. Xie, “Adaptive control of full-state constrained high-order nonlinear systems with time-varying powers,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 8, pp. 5189–5197, 2021.

    Article  Google Scholar 

  17. Y. D. Song and S. Y. Zhou, “Tracking control of uncertain nonlinear systems with deferred asymmetric time-varying full state constraints,” Automatica, vol. 98, pp. 314–322, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. N. Chen and C. C. Hua, “Adaptive full-state-constrained control of nonlinear systems with deferred constraints based on nonbarrier lyapunov function method,” IEEE Transactions on Cybernetics, vol. 52, no. 8, pp. 7634–7642, 2022.

    Article  Google Scholar 

  19. B. Yang, L. Cao, W. B. Xiao, D. Y. Yao, and R. Q. Lu, “Event-triggered adaptive neural control for multiagent systems with deferred state constraints,” Journal of Systems Science and Complexity, vol. 35, no. 3, pp. 973–992, 2021.

    Article  MathSciNet  MATH  Google Scholar 

  20. K. Zhao, L. Chen, and C. L. P. Chen, “Event-based adaptive neural control of nonlinear systems with deferred constraint,” IEEE Transactions on Systems Man Cybernetics-Systems, vol. 52, no. 10, pp. 6273–6282, 2022.

    Article  Google Scholar 

  21. R. Postoyan, P. Tabuada, D. Nesic, and A. Anta, “A framework for the event-triggered stabilization of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 60, no. 4, pp. 982–996, April 2015.

    Article  MathSciNet  MATH  Google Scholar 

  22. L. T. Xing, C. Y. Wen, Z. T. Liu, H. Y. Su, and J. P. Cai, “Event-triggered adaptive control for a class of uncertain nonlinear systems,” IEEE Transactions on Automatic Control, vol. 62, no. 4, pp. 2071–2076, April 2017.

    Article  MathSciNet  MATH  Google Scholar 

  23. H. Q. Wang, S. Ling, P. X. Liu, and Y. X. Li, “Control of high-order nonlinear systems under error-to-actuator based event-triggered framework,” International Journal of Control, vol. 95, no. 10, pp. 2758–2770, 2022.

    Article  MathSciNet  MATH  Google Scholar 

  24. J. A. Zhang, C. E. Ren, and Q. X. Fu, “Adaptive event-triggered control for stochastic nonlinear multi-agent systems with unknown control directions,” International Journal of Control, Automation, and Systems, vol. 19, no. 9, pp. 2950–2958, September 2021.

    Article  Google Scholar 

  25. J. Cheng, J. H. Park, and Z.G. Wu, “Observer-based asynchronous control of nonlinear systems with dynamic event-based try-once-discard protocol,” IEEE Transactions on Cybernetics, vol. 52, no. 12, pp. 12638–12648, 2022.

    Article  Google Scholar 

  26. J. Cheng, L. D. Liang, J. H. Park, H. C. Yan, and K. Z. Li, “A dynamic event-triggered approach to state estimation for switched memristive neural networks with nonhomogeneous sojourn probabilities,” IEEE Transactions on Circuits and Systems-I, vol. 68, no. 12, pp. 4924–4934, 2021.

    Article  Google Scholar 

  27. B. Yang and W. Lin, “Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback,” IEEE Transactions on Automatic Control, vol. 49, no. 7, pp. 1069–1080, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  28. C. Qian and W. Lin, “Non-lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization,” Systems and Control Letters, vol. 42, no. 3, pp. 185–200, March 2001.

    Article  MathSciNet  MATH  Google Scholar 

  29. C. L. Wang and Y. Lin, “Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems,” Automatica, vol. 54, pp. 16–24, April 2015.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Liuliu Zhang.

Additional information

Conflict of Interest

The authors declare that there is no competing financial interest or personal relationship that could have appeared to influence the work reported in this paper.

Liuliu Zhang received her Ph.D. degree in electrical engineering from Yanshan University in 2018. She is currently an Associate Professor in Yanshan University. Her current research interests include nonlinear system control, intelligent control of networked interconnected system, and multi-robot cooperative control.

Yue Guo received her B.S. degree in automation from Shanxi University in 2020. She is currently working toward an M.S. degree in Yanshan University. Her current research interests include nonlinear system control.

Changchun Hua received his Ph.D. degree in electrical engineering from Yanshan University in 2005. He is currently a Full Professor with Yanshan University. His current research interests include nonlinear control systems, control systems design over network, teleoperation systems, and intelligent control.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, L., Guo, Y. & Hua, C. Adaptive Event-triggered Control for High-order Nonlinear Systems with Deferred Asymmetric Full-state Constraints. Int. J. Control Autom. Syst. 21, 2183–2190 (2023). https://doi.org/10.1007/s12555-022-0265-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-022-0265-7

Keywords

Navigation