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

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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.

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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 

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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.

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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

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  1. Lisai Gao
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Correspondence to Jingqi Fu.

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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

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

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