Event-based Adaptive Output Feedback Prescribed Performance Control for a Class of Switched Nonlinear Systems with Unknown Control Directions

Abstract

An event-triggered adaptive tracking control problem is investigated for a class of switched nonstrictfeedback nonlinear systems with unknown control directions and switching signals. With a linear observer, the output feedback stabilization is achieved under arbitrary switching. The key advantages of the proposed control strategy are that the tracking prescribed performance is ensured regardless of the unknown control directions. Only one tuning parameter needs to be estimated during the recursive process. Moreover, with a varying threshold, a common event-triggered mechanism is developed. Based on the Lyapunov stability theory and the dynamic surface backstepping technique, the developed control method theoretically proves that under arbitrary switching, all signals of the resulting closed-loop switched system are bounded and the tracking error can converge to a small neighborhood of the origin within the prescribed bounds. The Zeno behavior is also avoided. The effectiveness and feasibility are demonstrated by two examples.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    G. Chesi, “On the minimum stable commutation time for switching nonlinear systems,” IEEE Trans. on Automatic Control, vol. 54, no. 6, pp. 1284–1289, June 2009.

    MathSciNet  Article  Google Scholar 

  2. [2]

    W. P. Dayawansa and C. F. Martin, “A converse Lyapunov theorem for a class of dynamical systems which undergo switching,” IEEE Trans. on Automatic Control, vol. 44, no. 4, pp. 751–760, Apirl 1999.

    MathSciNet  Article  Google Scholar 

  3. [3]

    O. Homaee, A. Zakariazadeh, and S. Jadid, “Real-time voltage control algorithm with switched capacitors in smart distribution system in presence of renewable generations,” Electrical Power and Energy Systems, vol. 54, pp. 187–197, January 2014.

    Article  Google Scholar 

  4. [4]

    A. S. Morse, “Supervisory control of families of linear setpoint controllers Part I. Exact matching,” IEEE Trans. on Automatic Control, vol. 41, no. 10, pp. 1413–1431, October 1989.

    Article  Google Scholar 

  5. [5]

    L. X. Zhang and P. Shi, “Stability, l2-gain and asynchronous H¥ control of discrete-time switched systems with average dwell time,” IEEE Trans. on Automatic Control, vol. 54, no. 9, pp. 2192–2199, September 2009.

    MathSciNet  Article  Google Scholar 

  6. [6]

    J. P. Hespanha, “Uniform stability of switched linear systems: Extensions of LaSalle’s Invariance Principle,” IEEE Trans. on Automatic Control, vol. 49, no. 4, pp. 470–482, April 2004.

    MathSciNet  Article  Google Scholar 

  7. [7]

    X. D. Zhao, L. X. Zhang, P. Shi, and M. Liu, “Stability and stabilization of switched linear systems with modedependent average dwell time,” IEEE Trans. on Automatic Control, vol. 57, no. 7, pp. 1809–1815, July 2012.

    MathSciNet  Article  Google Scholar 

  8. [8]

    J. C. Geromel, P. Colaneri, and P. Bolzern, “Dynamic output feedback control of switched linear systems,” IEEE Trans. on Automatic Control, vol. 53, no. 3, pp. 720–733, April 2008.

    MathSciNet  Article  Google Scholar 

  9. [9]

    D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, no. 5, pp. 59–70, October 1999.

    Article  Google Scholar 

  10. [10]

    C. Y. Wang and X. H. Jiao, “Observer-based adaptive arbitrary switching fuzzy tracking control for a class of switched nonlinear systems,” International Journal of Control, Automation and Systems, vol. 13, no. 4, pp. 823–830, August 2015.

    Article  Google Scholar 

  11. [11]

    Z. L. Liu, B. Chen, and C. Lin, “Output-feedback control design for switched nonlinear systems: adaptive neural backstepping approach,” Information Sciences, vol. 457-458, pp. 62–75, August 2018.

    MathSciNet  Article  Google Scholar 

  12. [12]

    D. Zhai, L. W. An, J. X. Dong, and Q. L. Zhang, “Switched adaptive fuzzy tracking control for a class of switched nonlinear systems under arbitrary switching,” IEEE Trans. on Fuzzy Systems, vol. 26, no. 2, pp. 585–597, April 2018.

    Article  Google Scholar 

  13. [13]

    S. J. Yoo, “Adaptive tracking control for uncertain switched nonlinear systems in nonstrict-feedback form,” Journal of the Franklin Institute, vol. 353, no. 6, pp. 1409–1422, April 2016.

    MathSciNet  Article  Google Scholar 

  14. [14]

    Y. L. Liu and H. J. Ma, “Adaptive fuzzy tracking control of nonlinear switched stochastic systems with prescribed performance and unknown control directions,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 50, no. 2, pp. 590–599, 2020.

    Article  Google Scholar 

  15. [15]

    L. L. Zhang, C. C. Hua, H. N. Yu, and X. P. Guan, “Decentralized adaptive control of switched interconnected highorder nonlinear systems with unknown control direction and time-delay,” International Journal of Control, vol. 92, no. 4, pp. 875–885, May 2019.

    MathSciNet  Article  Google Scholar 

  16. [16]

    Y. Dong, Z. X. Yu, S. G. Li, and F. F. Li, “Adaptive output feedback tracking control for switched non-strict-feedback nonlinear systems with unknown control direction and asymmetric saturation actuators,” IET Control Theory & Applications, vol. 11, no. 15, pp. 2539–2548, October 2017.

    MathSciNet  Article  Google Scholar 

  17. [17]

    H. J. Ma, Y. L. Liu and D. Ye, “Adaptive output feedback tracking control for non-linear switched stochastic systems with unknown control directions,” IET Control Theory & Applications, vol. 12, no. 4, pp. 484–494, March 2018.

    MathSciNet  Article  Google Scholar 

  18. [18]

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

    MathSciNet  Article  Google Scholar 

  19. [19]

    K. J. Åström and B. Bernhardsson, “Comparison of periodic and event based sampling for first-order stochastic systems,” Proceedings of the 14th IFAC World Congress, pp. 301–306, 1999.

    Google Scholar 

  20. [20]

    L. T. Xing, C. Y. Wen, Z. T. Liu, H. Y. Su, and J. P. Cai, “Event-triggered output feedback control for a class of uncertain nonlinear systems,” IEEE Trans. on Automatic Control, vol. 64, no. 1, pp. 290–297, January 2019.

    MathSciNet  Article  Google Scholar 

  21. [21]

    X. Q. Xiao, L. Zhou, D. W. C. Ho, and G. P. Lu, “Eventtriggered control of continuous-time switched linear systems,” IEEE Trans. on Automatic Control, vol. 64, no. 4, pp. 1710–1717, April 2019.

    MathSciNet  Article  Google Scholar 

  22. [22]

    Y. W. Qi, Z. Cao, and X. L. Li, “Decentralized eventtriggered H¥ control for switched systems with network communication delay,” Journal of the Franklin Institute, vol. 356, no. 3, pp. 1424–1445, February 2019.

    MathSciNet  Article  Google Scholar 

  23. [23]

    G. Q. Ma and P. R. Pagilla, “Periodic event-triggered dynamic output feedback control of switched systems,” Nonlinear Analysis: Hybrid Systems, vol. 31, pp. 247–264, February 2019.

    MathSciNet  MATH  Google Scholar 

  24. [24]

    H. C. Yan, H. Zhang, X. S. Zhan, Y. Y. Wang, S. M. Chen, and F. W. Yang, “Event-triggered sliding mode control of switched neural networks with mode-dependent average dwell time,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2019. DOI: 10.1109/TSMC.2019.2894984.

    Google Scholar 

  25. [25]

    X. X. Liu, X. J. Su, P. Shi, S. K. Nguang, and C. Shen, “Fault detection filtering for nonlinear switched systems via event-triggered communication approach,” Automatica, vol. 101, pp. 365–376, March 2019.

    MathSciNet  Article  Google Scholar 

  26. [26]

    S. P. Wen, Z. G. Zeng, M. Z. Q. Chen, and T. W. Huang, “Synchronization of switched neural networks with communication delays via the event-triggered control,” IEEE Trans. on Neural Networks and Learning Systems, vol. 28, no. 10, pp. 2334–2343, October 2017.

    MathSciNet  Article  Google Scholar 

  27. [27]

    L. H. Peng and Z. D. Ai, “Event-triggered stabilisation for continuous-time switched non-linear systems under switching constraints,” IET Control Theory & Applications, vol. 13, no. 8, pp. 1182–1186, May 2019.

    MathSciNet  Article  Google Scholar 

  28. [28]

    S. Q. Zheng, P. Shi, S. Y. Wang, and Y. Shi, “Event triggered adaptive fuzzy consensus for interconnected switched multiagent systems,” IEEE Trans. on Fuzzy Systems, vol. 27, no. 1, pp. 144–158, January 2019.

    Article  Google Scholar 

  29. [29]

    W. C. Zou and Z. R. Xiang, “Event-triggered leaderfollowing consensus of nonlinear multi-agent systems with switched dynamics,” IET Control Theory & Applications, vol. 13, no. 9, pp. 1222–1228, June 2019.

    MathSciNet  Article  Google Scholar 

  30. [30]

    X. Huo, L. Ma, X. D. Zhao, and G. D. Zong, “Eventtriggered adaptive fuzzy output feedback control of MIMO switched nonlinear systems with average dwell time,” Applied Mathematics and Computation, vol. 365, pp. 1–16, January 2020.

    Article  Google Scholar 

  31. [31]

    C. C. Wang and G. H. Yang, “Observer-based adaptive prescribed performance tracking control for nonlinear systems with unknown control direction and input saturation,” Neurocomputing, vol. 284, no. 5, pp. 17–26, April 2018.

    Article  Google Scholar 

  32. [32]

    Y. M. Li, S. C. Tong, L. Liu, and G. Feng, “Adaptive outputfeedback control design with prescribed performance for switched nonlinear systems,” Automatica, vol. 80, pp. 225–231, June 2017.

    MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Chunyan Wang.

Additional information

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

Recommended by Associate Editor Mathiyalagan Kalidass under the direction of Editor Jessie (Ju H.) Park. This research was supported by the Foundation of Hebei province Education Department (Grant No. QN2016076) and key research and development technology projects (Grant No. 17227401D).

Chunyan Wang received her Ph.D. degree in Control Science and Control Engineering from Yanshan University in 2015. She is a teacher in College of Sciences of Yanshan University. Her research interests include adaptive arbitrary switching control, asynchronous control and event-triggered control of switched systems.

Mengqi Zhang received her B.S. degree in Mathematics and Applied Mathematics from Changzhi University, China, in 2017. She is currently pursuing an M.S. degree in College of Sciences at Yanshan University. Her current research interests include nonlinear adaptive control, event-triggered control and their applications to switched nonlinear systems.

Huan Li received her B.S. degree in Applied Mathematics from Tangshan Normal University, China in 2018. She is currently pursuing an M.S. degree in College of Sciences at Yanshan University. Her current research interests include sampled-data control of switched systems.

Na Wang received her Ph.D. degree in Instrumental Science and technology from Yanshan University in 2011. She is a teacher in College of the electrical engineering of Yanshan University. Her research interests include signal processing and intelligent agriculture.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Zhang, M., Li, H. et al. Event-based Adaptive Output Feedback Prescribed Performance Control for a Class of Switched Nonlinear Systems with Unknown Control Directions. Int. J. Control Autom. Syst. 18, 2482–2491 (2020). https://doi.org/10.1007/s12555-019-0868-9

Download citation

Keywords

  • Arbitrary switching
  • event-triggered control
  • prescribed performance
  • switched nonlinear systems
  • unknown control directions