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Lyapunov-based event-triggered control for nonlinear plants subject to disturbances and transmission delays

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Abstract

This paper studies event-triggered control for disturbed nonlinear systems. A new dual-stage Lyapunov-based event-triggering condition is proposed to cope with the time-varying transmission delays. In the first stage, the ratio of Lyapunov function values at the last two triggering instants is calculated. Then based on the ratio, the corresponding threshold function is selected from two candidate forms. It is proved that the designed event-triggered control system is input-to-state practically stable with respect to the measurement errors and disturbances. Moreover, Zeno behavior is excluded successfully by calculating the lower bound of the minimum inter-event times. Finally, a simulation example is provided to show the feasibility and the effectiveness of the proposed approach.

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References

  1. Carnevale D, Teel A R, Nešić D D. Further results on stability of networked control systems: a Lyapunov approach. In: Proceedings of 2007 American Control Conference, New York, 2007. 1741–1746

    Google Scholar 

  2. °Astr¨om K J, Bernhardsson B. Comparison of periodic and event based sampling for first-order stochastic systems. In: Proceedings of the 14th IFAC World Congress, Beijing, 1999. 301–306

    Google Scholar 

  3. Dorf R C, Farren M, Phillips C. Adaptive sampling frequency for sampled-data control systems. IRE Trans Automat Contr, 1962, 7: 38–47

    Article  Google Scholar 

  4. Zhang B L, Han Q L, Zhang X M. Recent advances in vibration control of offshore platforms. Nonlin Dyn, 2017, 89: 755–771

    Article  Google Scholar 

  5. Zhang B L, Han Q L, Zhang X M. Event-triggered H1 reliable control for offshore structures in network environments. J Sound Vib, 2016, 368: 1–21

    Article  Google Scholar 

  6. Wang J, Zhang X M, Han Q L. Event-triggered generalized dissipativity filtering for neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst, 2016, 27: 77–88

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. Garcia E, Antsaklis P J. Model-based event-triggered control for systems with quantization and time-varying network delays. IEEE Trans Automat Contr, 2013, 58: 422–434

    Article  MathSciNet  Google Scholar 

  9. Mousavi S H, Ghodrat M, Marquez H J. Integral-based event-triggered control scheme for a general class of non-linear systems. IET Control Theory Appl, 2015, 9: 1982–1988

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. 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 (CDC), Grand Wailea, 2012. 3270–3285

    Google Scholar 

  12. 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 

  13. Zhang D, Han Q L, Jia X. Network-based output tracking control for T-S fuzzy systems using an event-triggered communication scheme. Fuzzy Sets Syst, 2015, 273: 26–48

    Article  MathSciNet  Google Scholar 

  14. Chen X, Hao F. Observer-based event-triggered control for certain and uncertain linear systems. IMA J Math Control Inf, 2013, 30: 527–542

    Article  MathSciNet  Google Scholar 

  15. Heemels W P M H, Donkers M C F, Teel A R. Periodic event-triggered control for linear systems. IEEE Trans Automat Contr, 2013, 58: 847–861

    Article  MathSciNet  Google Scholar 

  16. Mahmoud M S, Memon A M. Aperiodic triggering mechanisms for networked control systems. Inf Sci, 2015, 296: 282–306

    Article  MathSciNet  Google Scholar 

  17. Guinaldo M, Dimarogonas D V, Johansson K H, et al. Distributed event-based control strategies for interconnected linear systems. IET Contr Theor Appl, 2013, 7: 877–886

    Article  MathSciNet  Google Scholar 

  18. Abdelrahim M, Postoyan R, Daafouz J, et al. Input-to-state stabilization of nonlinear systems using event-triggered output feedback controllers. In: Proceedings of European Control Conference (ECC), Linz, 2015. 2180–2185

    MATH  Google Scholar 

  19. Ge X H, Han Q L, Wang Z D. A threshold-parameter-dependent approach to designing distributed event-triggered H1 consensus filters over sensor networks. IEEE Trans Cybern, 2019, 49: 1148–1159

    Article  Google Scholar 

  20. Ge X H, Han Q L, Wang Z D. A dynamic event-triggered transmission scheme for distributed set-membership estimation over wireless sensor networks. IEEE Trans Cybern, 2019, 49: 171–183

    Article  Google Scholar 

  21. Peng C, Li F Q. A survey on recent advances in event-triggered communication and control. Inf Sci, 2018, 457–458: 113–125

    Article  MathSciNet  Google Scholar 

  22. 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 

  23. Ge X H, Yang F W, Han Q L. Distributed networked control systems: a brief overview. Inf Sci, 2017, 380: 117–131

    Article  Google Scholar 

  24. Ding L, Han Q L, Ge X H, et al. An overview of recent advances in event-triggered consensus of multiagent systems. IEEE Trans Cybern, 2018, 48: 1110–1123

    Article  Google Scholar 

  25. Borgers D P, Heemels W P M H. Event-separation properties of event-triggered control systems. IEEE Trans Automat Contr, 2014, 59: 2644–2656

    Article  MathSciNet  Google Scholar 

  26. Abdelrahim M, Postoyan R, Daafouz J, et al. Robust event-triggered output feedback controllers for nonlinear systems. Automatica, 2017, 75: 96–108

    Article  MathSciNet  Google Scholar 

  27. Dolk V S, Borgers D P, Heemels W P M H. Output-based and decentralized dynamic event-triggered control with guaranteed L p-gain performance and zeno-freeness. IEEE Trans Automat Contr, 2017, 62: 34–49

    Article  MathSciNet  Google Scholar 

  28. Yu H, Hao F. The existence of Zeno behavior and its application to finite-time event-triggered control. Sci China Inf Sci, 2020, 63: 139201

    Article  MathSciNet  Google Scholar 

  29. Liu T, Jiang Z P. A small-gain approach to robust event-triggered control of nonlinear systems. IEEE Trans Automat Contr, 2015, 60: 2072–2085

    Article  MathSciNet  Google Scholar 

  30. Yang D P, Ren W, Liu X D, et al. Decentralized event-triggered consensus for linear multi-agent systems under general directed graphs. Automatica, 2016, 69: 242–249

    Article  MathSciNet  Google Scholar 

  31. Velasco Garc´ıa M, Mart´ı Colom P, Bini E. On lyapunov sampling for event-driven controllers. In: Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, Shanghai 2009. 6238–6243

    Google Scholar 

  32. Wang X F, Lemmon M D. Event design in event-triggered feedback control systems. In: Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, 2008. 2105–2110

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  34. Zhang L G, Hao J R, Qiao J F. Input-to-state stability of coupled hyperbolic PDE-ODE systems via boundary feedback control. Sci China Inf Sci, 2019, 62: 042201

    Article  Google Scholar 

  35. Dolk V S, Tesi P, de Persis C, et al. Output-based event-triggered control systems under denial-of-service attacks. In: Proceedings of the 54th IEEE Conference on Decision and Control (CDC), Osaka, 2015. 4824–4829

    Google Scholar 

  36. Postoyan R, Anta A, Neˇsi´c D, et al. A unifying Lyapunov-based framework for the event-triggered control of nonlinear systems. In: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference Hilton Orlando Bonnet Creek, 2011. 2559–2564

    Chapter  Google Scholar 

  37. Tabuada P, Wang X F. Preliminary results on state-trigered scheduling of stabilizing control tasks. In: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, 2006. 282–287

    Google Scholar 

  38. Vangipuram L. Practical Stability of Nonlinear Systems. Singapore: World Scientific Publishing, 1990

    Google Scholar 

  39. 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  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573036, 61174057).

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Authors and Affiliations

  1. The Seventh Research Division, School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191, China

    Xiaoda Hu, Hao Yu & Fei Hao

  2. The Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6G1H9, Canada

    Hao Yu

Authors
  1. Xiaoda Hu
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  2. Hao Yu
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  3. Fei Hao
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Correspondence to Fei Hao.

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Hu, X., Yu, H. & Hao, F. Lyapunov-based event-triggered control for nonlinear plants subject to disturbances and transmission delays. Sci. China Inf. Sci. 63, 150211 (2020). https://doi.org/10.1007/s11432-019-2654-y

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