Skip to main content
SpringerLink
Log in

Ultimately Bounded \(\mathcal {L}_\infty\) Output Feedback Control of Event-Triggered Nonlinear Systems Under Cyber Attacks

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This paper studies output-based \(\mathcal {L}_\infty\) security control of nonlinear system under the event-triggered mechanism (ETM) and random deception attacks. Firstly, a general ETM is proposed, whose triggering threshold includes both of a plant-dependent term and a plant-independent constant. Unlike some existing ETMs having high triggering rates during steady stage or transient stage, the proposed ETM can keep a low triggering rate during the whole system-running time. By integrating effects of the ETM, Bernoulli-distribution deception attacks, and network-induced delays in a unified framework, a closed-loop T-S fuzzy system model is built. Then, ultimately bounded stability criteria are obtained with guaranteed \(\mathcal {L}_\infty\) performance. Next, sufficient conditions for designing dynamic output feedback fuzzy controller are derived. Finally, an example illustrates effectiveness of the proposed methods.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Zhang, X.M., Han, Q.L., Ge, X., Ding, D., Ding, L., Yue, D., Peng, C.: Networked control systems: a survey of trends and techniques. IEEE/CAA J. Autom. Sin. 7(1), 1–17 (2020)

    MathSciNet  Google Scholar 

  2. Peng, C., Sun, H., Yang, M., Wang, Y.L.: A survey on security communication and control for smart grids under malicious cyber attacks. IEEE Trans. Syst. Man Cybern.: Syst. 49(8), 1554–1569 (2019)

    Article  Google Scholar 

  3. Hu, S., Yuan, P., Yue, D., Dou, C., Cheng, Z., Zhang, Y.: Attack-resilient event-triggered controller design of DC microgrids under DoS attacks. IEEE Trans. Circuits Syst. I: Regul. Pap. 67(2), 699–710 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang, D., Wang, Q.G., Feng, G., Shi, Y., Vasilakos, A.V.: A survey on attack detection, estimation and control of industrial cyberphysical systems. ISA Trans. 116, 1–16 (2021)

    Article  Google Scholar 

  5. He, W., Mo, Z., Han, Q.L., Qian, F.: Secure impulsive synchronization in Lipschitz-type multi-agent systems subject to deception attacks. IEEE/CAA J. Autom. Sin. 7(5), 1326–1334 (2020)

    MathSciNet  Google Scholar 

  6. Weng, S., Yue, D., Dou, C.: Secure distributed optimal frequency regulation of power grid with time-varying voltages under cyberattack. Int. J. Robust Nonlinear Control 30(3), 894–909 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhao, H., Niu, Y., Jia, T.: Security control of cyber-physical switched systems under Round-Robin protocol: input-to-state stability in probability. Inf. Sci. 508, 121–134 (2020)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Dolk, V., Borgers, D., Heemels, W.: Output-based and decentralized dynamic event-triggered control with guaranteed lp-gain performance and zeno-freeness. IEEE Trans. Autom. Control 62, 34–49 (2017)

    Article  MATH  Google Scholar 

  10. Peng, C., Yang, T.C.: Event-triggered communication and \(H_{\infty }\) control co-design for networked control systems. Automatica 49(5), 1326–1332 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Borgers, D., Heemels, W.: Event-separation properties of event-triggered control systems. IEEE Trans. Autom. Control 59, 2644–2656 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, K., Tian, E., Liu, J., Wei, L., Yue, D.: Resilient control of networked control systems under deception attacks: a memory-event-triggered communication scheme. Int. J. Robust Nonlinear Control 30(4), 1534–1548 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  13. Xie, X.P., Zhou, Q., Yue, D., Li, H.: Relaxed control design of discrete-time takagi-sugeno fuzzy systems: an event-triggered real-time scheduling approach. IEEE Trans. Syst. Man Cybern.: Syst. 48(12), 2251–2262 (2018)

    Article  Google Scholar 

  14. Liu, J., Yin, T., Cao, J., Yue, D., Karimi, H.R.: Security control for T-S fuzzy systems with adaptive event-triggered mechanism and multiple cyber-attacks. IEEE Trans. Syst. Man Cybern.: Syst. 51(10), 6544–6554 (2021)

    Article  Google Scholar 

  15. Wu, Z., Xiong, J., Xie, M.: Improved event-triggered control for networked control systems subject to deception attacks. J. Frankl. Inst. 358(4), 2229–2252 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gu, Z., Yin, T., Ding, Z.: Path tracking control of autonomous vehicles subject to deception attacks via a learning-based event-triggered mechanism. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3056764

  17. Sun, Y., Yu, J., Yu, X., Gao, H.: Decentralized adaptive event-triggered control for a class of uncertain systems with deception attacks and its application to electronic circuits. IEEE Trans. Circuits Syst. I: Regul. Pap. 67(12), 5405–5416 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tian, E., Peng, C.: Memory-based event-triggering \(H_\infty\) load frequency control for power systems under deception attacks. IEEE Trans. Cybern. 50(11), 4610–4618 (2020)

    Article  Google Scholar 

  19. Wang, Y.L., Han, Q.L., Fei, M.R., Peng, C.: Network-based T-S fuzzy dynamic positioning controller design for unmanned marine vehicles. IEEE Trans. Cybern. 48(9), 2750–2763 (2018)

    Article  Google Scholar 

  20. Ge, H., Yue, D., Xie, X., Deng, S., Hu, S.: Security control of networked T-S fuzzy system under intermittent DoS jamming attack with event-based predictor. Int. J. Fuzzy Syst. 21(3), 700–714 (2019)

    Article  MathSciNet  Google Scholar 

  21. Moser, B.A., Natschlager, T.: On stability of distance measures for event sequences induced by level-crossing sampling. IEEE Trans. Signal Process. 62(8), 1987–1999 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lunze, J., Lehmann, D.: A state-feedback approach to event-based control. Automatica 46(1), 211–215 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Liu, J., Wang, Y., Cao, J., Yue, D., Xie, X.: Secure adaptive-event-triggered filter design with input constraint and hybrid cyber attack. IEEE Trans. Cybern. 51(8), 4000–4010 (2021)

    Article  Google Scholar 

  24. Zhao, D., Wang, Z., Han, Q.L., Wei, G.: Proportional-integral observer design for uncertain time-delay systems subject to deception attacks: an outlier-resistant approach. IEEE Trans. Syst. Man Cybern.: Syst. (2021). https://doi.org/10.1109/TSMC.2021.3117742

  25. Xie, X.P., Bu, C., Peng, C.: Multi-instant gain-scheduling stabilization of discrete-time takagi-sugeno fuzzy systems based on a time-variant balanced matrix approach. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2021.3089047

  26. Xie, X.P., Yue, D., Peng, C.: Relaxed real-time scheduling stabilization of discrete-time takagi-sugeno fuzzy systems via an alterable-weights-based ranking switching mechanism. IEEE Trans. Fuzzy Syst. 26(6), 3808–3819 (2018)

    Article  Google Scholar 

  27. Xie, X.P., Lu, J., Yue, D., Ding, D.W.: Enhanced fuzzy fault estimation of discrete-time nonlinear systems via a new real-time gain-scheduling mechanism. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2021.3107040

  28. Zou, L., Wang, Z., Han, Q.L., Zhou, D.: Ultimate boundedness control for networked systems with try-once-discard protocol and uniform quantization effects. IEEE Trans. Autom. Control 62(12), 6582–6588 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  29. Donkers, M.C.F., Heemels, W.P.M.H.: Output-based event-triggered control with guaranteed \(\cal{L}_{\infty }\) gain and improved and decentralized event-triggering. IEEE Trans. Autom. Control 57(6), 1362–1376 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  30. Ge, C., Yang, L., Zhao, Z., Zhang, J., Liu, Y.: Stochastic switched sampled-data control for uncertain fuzzy systems with packet dropout. Int. J. Fuzzy Syst. 23(1), 145–157 (2021)

    Article  Google Scholar 

  31. Bourahala, F., Guelton, K., Manamanni, N., Khaber, F.: Relaxed controller design conditions for Takagi-Sugeno systems with state time-varying delays. Int. J. Fuzzy Syst. 19(5), 1406–1416 (2017)

    Article  MathSciNet  Google Scholar 

  32. Dong, J., Yang, G.H.: Dynamic output feedback control synthesis for continuous-time T-S fuzzy systems via a switched fuzzy control scheme. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(4), 1166–1175 (2008)

    Article  Google Scholar 

  33. Gao, L., Fu, J., Li, F.: Output-based security control of NCSs under resilient event-triggered mechanism and DoS attacks. Int. J. Control Autom. Syst. 19(4), 1519–1527 (2021)

    Article  Google Scholar 

  34. Zhang, X.M., Han, Q.L.: A decentralized event-triggered dissipative control scheme for systems with multiple sensors to sample the system outputs. IEEE Trans. Cybern. 46(12), 2745–2757 (2016)

    Article  Google Scholar 

  35. Guan, X.P., Chen, C.L.: Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays. IEEE Trans. Fuzzy Syst. 12(2), 236–249 (2004)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China under Grant 61703146; Scientific Project in Henan Province under Grant 202102110126; Backbone Teacher in Henan Province under Grant 2020GGJS048.

Author information

Authors and Affiliations

  1. School of Mechatronics Engineering and Automation, Shanghai University, Shanghai, 200444, People’s Republic of China

    Lisai Gao & Jingqi Fu

  2. College of Sciences, Henan Agricultural University, Zhengzhou, 450002, People’s Republic of China

    Fuqiang Li

Authors
  1. Lisai Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fuqiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingqi Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jingqi Fu.

Ethics declarations

Conflict of interest

The authors declare they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, L., Li, F. & Fu, J. Ultimately Bounded \(\mathcal {L}_\infty\) Output Feedback Control of Event-Triggered Nonlinear Systems Under Cyber Attacks. Int. J. Fuzzy Syst. 24, 3532–3543 (2022). https://doi.org/10.1007/s40815-022-01346-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-022-01346-4

Keywords

Search

Navigation