Advertisement

Sampling-based Event-triggered and Self-triggered Control for Linear Systems

  • Jun Chen
  • Yuan FanEmail author
  • Chengxiao Zhang
  • Cheng Song
Article
  • 2 Downloads

Abstract

This work considers the event-triggered and self-triggered control for linear systems with periodic sampling schemes. An event-triggered control using sampled states is proposed. The asymptotic stability of the closed-loop system is guaranteed by a condition in terms of a linear matrix inequality. Moreover, a self-triggered control with sampling is presented and the next control task release time is predicted based on the current sampled data. It is noted that by introducing the periodic sampling scheme, Zeno behaviors can be naturally avoided in both of the algorithms. Finally, simulation results are provided to illustrate the theoretical effectiveness.

Keywords

Event-triggered linear systems sampling-based self-triggered 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. [1]
    X. P. Xie, D. Yue, and P. Chen, “Multi-instant switching control of nonlinear networked systems under unreliable wireless digital channels,” Journal of the Franklin Institute-Engineering and Appled Mathematics, vol. 354, no. 9, pp. 3872–3884, June 2017.MathSciNetCrossRefGoogle Scholar
  2. [2]
    T. Wang, H. J. Gao, and J. B. Qiu, “A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control,” IEEE Transactions on Neural Networks Learning System, vol. 27, no. 99, pp. 416–425, April 2015.MathSciNetGoogle Scholar
  3. [3]
    X. F. Wang and M. D. Lemmon, “Self-triggered feedback control systems with finite-gain L2 stability,” IEEE Transactions on Automatic Control, vol. 54, no. 3, pp. 452–467, March 2009.MathSciNetCrossRefGoogle Scholar
  4. [4]
    X. F. Wang and M. D. Lemmon, “Event-triggering in distributed networks control systems,” IEEE Transactions on Automatic Control, vol. 56, no. 3, pp. 586–601, March 2011.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Y. Fan, G. Feng, Y. Wang, and C. Song, “Distributed event-triggered control of multi-agent systems with combinational measurements,” Automatica, vol. 49, no. 2, pp. 671–675, February 2013.MathSciNetCrossRefGoogle Scholar
  6. [6]
    W. F. Hu, L. Liu, and G. Feng, “Consessus of linear multi-agent systems by distributed event-triggered strategy,” IEEE Transactions on Cybernetics, vol. 46, no. 1, pp. 148–157, Feburary 2015.CrossRefGoogle Scholar
  7. [7]
    P. Tabuada, “Event-triggered real-time scheduling of stabilizing control tasks,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1680–1685, September 2007.MathSciNetCrossRefGoogle Scholar
  8. [8]
    A. Anto and P. Tabuada, “To sample or not to sample: self-triggered control for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 55, no. 9, pp. 2030–2042, October 2010.MathSciNetCrossRefGoogle Scholar
  9. [9]
    X. P. Xie, Q. Zhou, D. Yue, and H. Y. Li, “Relaxed control design of discrete-time Takagi-Sugeno fuzzy systems: an event-triggered real-time scheduling approach,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 12, pp. 2251–2262, October 2018.CrossRefGoogle Scholar
  10. [10]
    F. Q. Li, L. S. Gao, G. S. Dou, and B. Z. Zheng, “Dual-side event-triggered output feedback H8 control for NCS with communication delays,” International Journal of Control, Automation, and Systems, vol. 16, no. 1, pp. 108–119, March 2018.CrossRefGoogle Scholar
  11. [11]
    C. Liu and F. Hao, “Dynamic output-feedback control for linear systems by using event-triggered quantisation,” IET Control Theory and Application, vol. 9, no. 8, pp. 1254–1263, May 2015.MathSciNetCrossRefGoogle Scholar
  12. [12]
    M. Mazo, A. Anta, and P. Tabuada, “ISS self-triggered implementation of linear controllers,” Automatica, vol. 46, no. 8, pp. 1310–1314, June 2010.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Y. Fan, Y. Yang, and Y. Zhang, “Sampling-based event-triggered consensus for multi-agent systems,” Neurocom-puting, vol. 191, pp. 141–147, May 2016.CrossRefGoogle Scholar
  14. [14]
    A. D. Ames and S. Sastry, “Characterization of zeno behavior in hybrid systems using homological methods,” Proc. of American Control Conference, pp. 1160–1165, June 2005.Google Scholar
  15. [15]
    Y. Fan, S. Wang, and C. Song, “Zeno-free event-triggered consensus using sampled data.” Proc. of Chinese Control Conference, pp. 7039–7043, July 2015.Google Scholar
  16. [16]
    X. Chen and F. Hao, “Periodic event-triggered state-feedback and output-feedback control for linear systems,” International Journal of Control, Automation, and Systems, vol. 13, no. 4, pp. 779–787, May 2015.CrossRefGoogle Scholar
  17. [17]
    A. Sahoo, V. Narayanan, and S. Jagannathan, “A min-max approach to event-triggered and self-triggered sampling and regulation of linear systems,” IEEE Transactions on Industrial Electronics, vol. 66, no. 7, pp. 5433–5440, July 2019.CrossRefGoogle Scholar
  18. [18]
    K. Masako, “Event-triggered control with self-triggered sampling for discrete-time uncertain systems,” IEEE Transactions on Automatic Control, vol. 64, no. 3, pp. 1273–1279, March 2019.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Y. Fan, L. Liu, G. Feng, and Y. Wang, “Self-triggered consensus for multi-agent systems with Zeno-free triggers,” IEEE Transactions on Automatic Control, vol. 60, no. 10, pp. 2779–2784, October 2015.MathSciNetCrossRefGoogle Scholar
  20. [20]
    Y. Fan, C. X. Zhang, and C. Song, “Sampling-based self-triggered coordination control for multi-agent systems with application to distributed generators,” International Journal of System Science, vol. 49, no. 15, pp. 3048–3062, September 2018.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Y. Fan and J. Y. Yang, “Average consensus of multi-agent systems with self-triggered controllers,” Neurocomputing, vol. 177, pp. 33–39, Feburary 2016.CrossRefGoogle Scholar
  22. [22]
    X. Chen and F. Hao, “Observer-based event-triggered control for certain and uncertain linear systems,” IMA Journal of Mathematical Control and Information, vol. 30, no. 4, pp. 527–542, December 2013.MathSciNetCrossRefGoogle Scholar
  23. [23]
    C. Peng and Q. L. Han, “Output-based event-triggered H8 control for sampled-data control systems with nonuniform sampling,” Proc. of 2013 American Control Conference, pp. 1727–1732, June 2013.CrossRefGoogle Scholar
  24. [24]
    A. Tanwani, C. Prieur, and M. Fiacchini, “Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization,” Systems and Control Letters, vol. 94, pp. 46–56, August 2016.MathSciNetCrossRefGoogle Scholar
  25. [25]
    Z. B. Lu, G. Guo, G. L. Wang, and G. Q. Yang, “Hybrid random event-triggered and time-triggered control and scheduling,” International Journal of Control, Automation, and Systems, vol. 14, no. 3, pp. 845–853, June 2016.CrossRefGoogle Scholar
  26. [26]
    E. E. Yaz, “Linear matrix inequalities in system and control theory,” Proc. of the IEEE, pp. 2473–2474, December 1998.Google Scholar
  27. [27]
    L. Yu, Robust Control: The Method to Solve Linear Matrix Inequality, Bejing, 2002.Google Scholar
  28. [28]
    S. Y. Zhang and L. Q. Gao, Method Control Theory, Bejing, 2005.Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  • Jun Chen
    • 1
  • Yuan Fan
    • 1
    Email author
  • Chengxiao Zhang
    • 1
  • Cheng Song
    • 2
  1. 1.Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Electrical Engineering and AutomationAnhui UniversityHefeiChina
  2. 2.School of AutomationNanjing University of Science and TechnologyNanjingChina

Personalised recommendations