Skip to main content
Springer Nature Link
Log in

Event-based triggering mechanisms for nonlinear control systems

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

This study examines triggered implementations of stabilizing controllers for general nonlinear systems. By using perturbation theory and Taylor’s theorem, we propose new event-triggering and self-triggering mechanisms for general nonlinear control systems that are not necessarily input-to-state stable with respect to measurement errors. Both mechanisms are presented based on mild conditions and can ensure the uniform ultimate boundedness of the solutions of the resulting closed-loop control systems. The ultimate bounds can be made arbitrarily small by adjusting the design parameters. The effectiveness of the theoretical results is illustrated by simulations.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Yu H, Antsaklis P J. Event-triggered output feedback control for networked control systems using passivity: achieving stability in the presence of communication delays and signal quantization. Automatica, 2013, 49: 30–38

    Article  MathSciNet  Google Scholar 

  2. Wang X F, Lemmon M D. Event-triggering in distributed networked control systems. IEEE Trans Automat Contr, 2011, 56: 586–601

    Article  MathSciNet  Google Scholar 

  3. Wang X F, Lemmon M. On event design in event-triggered feedback systems. Automatica, 2011, 47: 2319–2322

    Article  MathSciNet  Google Scholar 

  4. Heemels W P M H, Sandee J H, van Den Bosch P P J. Analysis of event-driven controllers for linear systems. Int J Control, 2008, 81: 571–590

    Article  MathSciNet  Google Scholar 

  5. Tabuada P. Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans Automat Contr, 2007, 52: 1680–1685

    Article  MathSciNet  Google Scholar 

  6. Selivanov A, Fridman E. Event-triggered H∞ control: a switching approach. IEEE Trans Automat Contr, 2016, 61: 3221–3226

    Article  MathSciNet  Google Scholar 

  7. Zhang X M, Han Q L, Zhang B L. An overview and deep investigation on sampled-data-based event-triggered control and filtering for networked systems. IEEE Trans Ind Inf, 2017, 13: 4–16

    Article  Google Scholar 

  8. Gu Z, Yue D, Tian E G. On designing of an adaptive event-triggered communication scheme for nonlinear networked interconnected control systems. Inf Sci, 2018, 422: 257–270

    Article  Google Scholar 

  9. Cuenca A, Antunes D J, Castillo A, et al. Periodic event-triggered sampling and dual-rate control for a wireless networked control system with applications to UAVs. IEEE Trans Ind Electron, 2019, 66: 3157–3166

    Article  Google Scholar 

  10. Brunner F D, Heemels W P M H, Allgöwer F. Event-triggered and self-triggered control for linear systems based on reachable sets. Automatica, 2019, 101: 15–26

    Article  MathSciNet  Google Scholar 

  11. Borgers D P, Postoyan R, Anta A, et al. Periodic event-triggered control of nonlinear systems using overapproximation techniques. Automatica, 2018, 94: 81–87

    Article  MathSciNet  Google Scholar 

  12. Khashooei B A, Antunes D J, Heemels W P M H. A consistent threshold-based policy for event-triggered control. IEEE Control Syst Lett, 2018, 2: 447–452

    Article  Google Scholar 

  13. Abdelrahim M, Postoyan R, Daafouz J, et al. Co-design of output feedback laws and event-triggering conditions for the L2-stabilization of linear systems. Automatica, 2018, 87: 337–344

    Article  Google Scholar 

  14. Li F Z, Liu Y G. Global practical tracking with prescribed transient performance for inherently nonlinear systems with extremely severe uncertainties. Sci China Inf Sci, 2019, 62: 022204

    Article  MathSciNet  Google Scholar 

  15. Zheng C, Li L, Wang L Y, et al. How much information is needed in quantized nonlinear control? Sci China Inf Sci, 2018, 61: 092205

    Article  MathSciNet  Google Scholar 

  16. Heemels W P M H, Johansson K H, Tabuada P. An introduction to event-triggered and self-triggered control. In: Proceedings of the 51st IEEE Conference on Decision and Control, Maui, 2012. 3270–3285

    Google Scholar 

  17. Girard A. Dynamic triggering mechanisms for event-triggered control. IEEE Trans Automat Contr, 2015, 60: 1992–1997

    Article  MathSciNet  Google Scholar 

  18. Postoyan R, Tabuada P, Nesic D, et al. A framework for the event-triggered stabilization of nonlinear systems. IEEE Trans Automat Contr, 2015, 60: 982–996

    Article  MathSciNet  Google Scholar 

  19. Sontag E, Teel A. Changing supply functions in input/state stable systems. IEEE Trans Automat Contr, 1995, 40: 1476–1478

    Article  MathSciNet  Google Scholar 

  20. Freeman R. Global internal stabilizability does not imply global external stabilizability for small sensor disturbances. IEEE Trans Automat Contr, 1995, 40: 2119–2122

    Article  MathSciNet  Google Scholar 

  21. Fah N C S. Input-to-state stability with respect to measurement disturbances for one-dimensional systems. ESAIM: Control Opt Calc Var, 1999, 4: 99–121

    MathSciNet  MATH  Google Scholar 

  22. Khalil H. Nonlinear Systems. 3rd ed. Upper saddle River: Prentice Hall, 2002

    MATH  Google Scholar 

  23. Wang X F, Lemmon M D. Self-triggered feedback control systems with finite-gain ℒ2 stability. IEEE Trans Automat Contr, 2009, 54: 452–467

    Article  MathSciNet  Google Scholar 

  24. Mazo Jr M, Anta A, Tabuada P. An ISS self-triggered implementation of linear controllers. Automatica, 2010, 46: 1310–1314

    Article  MathSciNet  Google Scholar 

  25. Anta A, Tabuada P. To sample or not to sample: self-triggered control for nonlinear systems. IEEE Trans Automat Contr, 2010, 55: 2030–2042

    Article  MathSciNet  Google Scholar 

  26. Anta A, Tabuada P. Exploiting isochrony in self-triggered control. IEEE Trans Automat Contr, 2012, 57: 950–962

    Article  MathSciNet  Google Scholar 

  27. Lin Y D, Sontag E D, Wang Y. A smooth converse Lyapunov theorem for robust stability. SIAM J Control Opt, 1996, 34: 124–160

    Article  MathSciNet  Google Scholar 

  28. Mazo M, Tabuada P. Decentralized event-triggered control over wireless sensor/actuator networks. IEEE Trans Automat Contr, 2011, 56: 2456–2461

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by National Science Foundation for Young Scientists of China (Grant No. 61803069) and Fundamental Research Funds for the Central Universities of China (Grant Nos. DUT17GJ203, DUT17RC(3)088).

Author information

Authors and Affiliations

  1. Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian, 116023, China

    Yongfeng Gao, Ximing Sun, Xian Du & Wei Wang

Authors
  1. Yongfeng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ximing Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xian Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xian Du.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, Y., Sun, X., Du, X. et al. Event-based triggering mechanisms for nonlinear control systems. Sci. China Inf. Sci. 63, 150209 (2020). https://doi.org/10.1007/s11432-019-2688-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-019-2688-1

Keywords