Skip to main content
SpringerLink
Log in

Improved Dynamic Event-Triggered Security Control for T–S Fuzzy LPV-PDE Systems via Pointwise Measurements and Point Control

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

Abstract

This paper investigates security control for linear parameter-varying partial differential equation systems under an improved dynamic event-triggered mechanism (DETM). Initially, based on the Takagi–Sugeno fuzzy model, the nonlinear terms of the considered systems are approximated. Then, pointwise measurements are introduced to reduce the number of sensors. To further abate the transmission channel congestion caused by the limited bandwidth, an improved DETM is offered. Besides, point fuzzy controller is constructed to save control costs by utilizing limited actuators. Especially, in the networked control framework, the appearance of attacks will pose a serious threat to the systems’ stability. To simulate complex forms of attacks, dual deception attacks are taken into account. Moreover, some appropriate parameter-dependent Lyapunov–Krasovskii functionals are employed to obtain correlated conditions that ensure the exponential stability of the target system. Finally, numerical and application examples are provided to verify the effectiveness of the proposed design methods. The average trigger rate in the two cases is reduced to 4.58% and 3.68%, respectively.

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
Fig. 9

Similar content being viewed by others

References

  1. Moura, S.J., Chaturvedi, N.A., Krstic, M.: PDE estimation techniques for advanced battery management systems: Part I: SOC estimation. In: Proceedings of the 2012 American Control Conference (ACC), pp. 559-565 (2012)

  2. Hashi, S.M., Tokhi, M.O., Darus, I.M.: Active vibration control of flexible structures using genetic optimisation. J. Low Freq. Noise Vib. Active 25(3), 195–207 (2006)

    Article  Google Scholar 

  3. Dong, Z.: Nonlinear state-feedback dissipation power level control for nuclear reactors. IEEE Trans. Nucl. Sci. 58(1), 241–257 (2010)

    Article  Google Scholar 

  4. Wang, Y.Y., Karimi, H.R., Yan, H.C.: An adaptive event-triggered synchronization approach for chaotic lur’e systems subject to aperiodic sampled data. IEEE Trans. Circuits Syst. II, Exp. Briefs 66(3), 442–446 (2019)

    Google Scholar 

  5. Wang, J.W., Wu, H.N.: Lyapunov-based design of locally collocated controllers for semi-linear parabolic PDE systems. J. Frankl. Inst. 351(1), 429–441 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Wu, H.N., Zhang, X.W.: Static output feedback stabilization for a linear parabolic PDE system with time-varying delay via mobile collocated actuator/sensor pairs. Automatica 117, 108993 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  7. Tsai, S.H., Wang, J.W., Song, E.S., Lam, H.K.: Robust \(H_{\infty }\) control for nonlinear hyperbolic PDE systems based on the polynomial fuzzy model. IEEE Trans. Cybern. 51(7), 3789–3801 (2019)

    Article  Google Scholar 

  8. Do, M.H., Koenig, D., Theilliol, D.: Robust \(H_{\infty }\) proportional-integral observer-based controller for uncertain LPV system. J. Frankl. Inst. 357(4), 2099–2130 (2020)

    Article  MATH  Google Scholar 

  9. Lu, Q.G., Zhang, L.X., Shi, P., Karimi, H.R.: Control design for a hypersonic aircraft using a switched linear parameter-varying system approach. Proc. Inst. Mech. Eng. Part I-J. Syst. Control Eng. 227(1), 85–95 (2013)

    Article  Google Scholar 

  10. Bianchi, F.D., Mantz, R.J., Christiansen, C.F.: Gain scheduling control of variable-speed wind energy conversion systems using quasi-LPV models. Comput. Electr. Pract. 13(2), 247–255 (2005)

    Google Scholar 

  11. Schorsch, J., Laurain, V., Gilson, M.: Refined IV-based method for LPV partial differential equation model identification. In: Proceedings of the 2014 European Control Conference (ECC), pp. 2127-2132 (2014)

  12. Wu, C.F., Chen, B.S., Zhang, W.H.: Multiobjective control for nonlinear stochastic Poisson jump-diffusion systems via T-S fuzzy interpolation and Pareto optimal scheme. Fuzzy Sets Syst. 385, 148–168 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  13. Xie, X.P., Yue, D., Park, J.H., Li, H.Y.: Relaxed fuzzy observer design of discrete-time nonlinear systems via two effective technical measures. IEEE Trans. Fuzzy Syst. 26(5), 2833–2845 (2018)

    Article  Google Scholar 

  14. Jiang, Y.: Intermittent distributed control for a class of nonlinear reaction-diffusion systems with spatial point measurements. J. Frankl. Inst. 356(7), 3811–3830 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang, J.W., Wu, H.N.: Exponential pointwise stabilization of semilinear parabolic distributed parameter systems via the Takagi–Sugeno fuzzy PDE model. IEEE Trans. Fuzzy Syst. 26(1), 155–173 (2016)

    Article  Google Scholar 

  16. Wang, J.W., Liu, Y.Q., Sun, C.Y.: Pointwise exponential stabilization of a linear parabolic PDE system using non-collocated pointwise observation. Automatica 93, 197–210 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  17. Song, X.N., Wang, M., Zhang, Q.Y.: Takagi–Sugeno fuzzy-model-based event-triggered point control for semilinear partial differential equation systems using collocated pointwise measurements. Int. J. Robust Nonlinear Control 31(4), 1122–1144 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, W., Wang, T.C., Tong, S.C.: Event-triggered control for networked switched fuzzy time-delay systems with saturated inputs. Int. J. Fuzzy Syst. 21(5), 1455–1466 (2019)

    Article  MathSciNet  Google Scholar 

  19. Xia, J.W., Li, B.M., Su, S.F., Sun, W., Shen, H.: Finite-time command filtered event-triggered adaptive fuzzy tracking control for stochastic nonlinear systems. IEEE Trans. Fuzzy Syst. 29(7), 2242–2254 (2021)

    Article  Google Scholar 

  20. Tian, E.G., 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 

  21. Chen, B., Zou, Y.Y., Niu, Y.G.: Dynamic event-triggered sliding mode security control for Markovian jump systems: learning-based iteration optimization method. Int. J. Robust Nonlinear Control 32(5), 2500–2517 (2022)

    Article  MathSciNet  Google Scholar 

  22. Ge, X.H., Han, Q.L., Zhang, X.M., Ding, D.R.: Dynamic event-triggered control and estimation: a survey. Int. J. Control Autom. Syst. 18(6), 857–886 (2021)

    Google Scholar 

  23. Wang, H., Chen, X., Wang, J.: \(H_{\infty }\) sliding mode control for PDT-switched nonlinear systems under the dynamic event-triggered mechanism. Appl. Math. Comput. 412, 126474 (2022)

    MathSciNet  MATH  Google Scholar 

  24. Zhang, H., Cheng, P., Shi, L., Chen, J.: Optimal DoS attack scheduling in wireless networked control system. IEEE Trans. Control Syst. Technol. 24(3), 843–852 (2015)

    Article  Google Scholar 

  25. Qian, Y.J., He, D.Y., Wang, S., Chen, W., Yin, Z.Q., Guo, G.C., Han, Z.F.: Robust countermeasure against detector control attack in a practical quantum key distribution system. Optica 6(9), 1178–1184 (2019)

    Article  Google Scholar 

  26. Ding, D.R., Wang, Z.D., Ho, D.W.C., Wei, G.L.: Distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks. Automatica 78, 231–240 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  27. Li, T.F., Chang, X.H., Park, J.H.: Control design for parabolic PDE systems via T–S fuzzy model. IEEE Trans. Syst. Man Cybern. Syst. 52(6), 3671–3679 (2022)

    Article  Google Scholar 

  28. Ma, T., Cao, C.Y.: \(L_1\) adaptive control for general partial differential equation (PDE) systems. Int. J. Gen. Syst. 48(6), 656–689 (2019)

    Article  MathSciNet  Google Scholar 

  29. Zhang, X.W., Wu, H.N.: Fuzzy control design of nonlinear time-delay parabolic PDE systems under mobile collocated actuators and sensors. IEEE Trans. Cybern. 52(5), 3947–3956 (2020)

    Article  Google Scholar 

  30. Zong, G.D., Yang, D., Lam, J., Song, X.Q.: Fault-tolerant control of switched LPV systems: a bumpless transfer approach. IEEE Trans. Mech. 27(3), 1436–1446 (2021)

    Google Scholar 

  31. Zhang, B.Y., Xu, S.Y., Ma, Q., Zhang, Z.Q.: Output-feedback stabilization of singular LPV systems subject to inexact scheduling parameters. Automatica 104, 1–7 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  32. Hanema, J., Lazar, M., Tóth, R.: Heterogeneously parameterized tube model predictive control for LPV systems. Automatica 111, 108622 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  33. Gu, Z., Ahn, C.K., Yue, D., Xie, X.P.: Event-triggered \(H_{\infty }\) filtering for T-S fuzzy-model-based nonlinear networked systems with multisensors against DoS attacks. IEEE Trans. Cybern. 52(6), 5311–5321 (2022)

    Article  Google Scholar 

  34. Liu, J.L., Wang, Y.D., Cao, J.D., Yue, D., Xie, X.P.: Secure adaptive-event-triggered filter design with input constraint and hybrid cyber attack. IEEE Trans. Cybern. 51(8), 4000–4010 (2020)

    Article  Google Scholar 

  35. Song, X.N., Zhang, Q.Y., Song, S., Ahn, C.K.: Sampled-data-based event-triggered fuzzy control for PDE systems under cyber-attacks. IEEE Trans. Fuzzy Syst. 30(7), 2693–2705 (2022)

    Article  Google Scholar 

  36. Xing, M.Q., Wang, Y.Q., Zhuang, G.M., Zhang, M.S.: Dynamic event-based dissipative asynchronous control for T-S fuzzy singular Markov jump LPV systems against deception attacks. Nonlinear Dyn. 103(2), 1709–1731 (2021)

    Article  MATH  Google Scholar 

  37. Gu, K.Q., Chen, J., Kharitonov, V.L.: Stability of Time-Delay Systems. Springer, New York (2003)

    Book  MATH  Google Scholar 

  38. Kövari, T., Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Math. Gaz. 72(462), 333 (1988)

    Article  Google Scholar 

  39. Wang, Y.Y., Xie, L.H., De Souza, C.E.: Robust control of a class of uncertain nonlinear systems. Syst. Control Lett. 19(2), 139–149 (1992)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 62203153 and 61976081, in part by the Natural Science Fund for Excellent Young Scholars of Henan Province under Grant 202300410127, in part by Key Scientific Research Projects of Higher Education Institutions in Henan Province under Grant 22A413001, in part by Top Young Talents in Central Plains under Grant Yuzutong (2021) 44, in part by Technology Innovative Teams in University of Henan Province under Grant 23IRTSTHN012, in part by the Natural Science Fund for Young Scholars of Henan Province under Grant 222300420151, and in part by the Serbian Ministry of Education, Science and Technological Development (No. 451-03-68/2022-14/200108).

Author information

Authors and Affiliations

  1. School of Information Engineering, Henan University of Science and Technology, Kaiyuan Avenu, Luoyang, 471023, Henan, China

    Xiaona Song, Yulong Song & Shuai Song

  2. Faculty of Mechanical and Civil Engineering, University of Kragujevac, 36000, Kraljevo, Serbia

    Vladimir Stojanovic

Authors
  1. Xiaona Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yulong Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vladimir Stojanovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shuai Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuai Song.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, X., Song, Y., Stojanovic, V. et al. Improved Dynamic Event-Triggered Security Control for T–S Fuzzy LPV-PDE Systems via Pointwise Measurements and Point Control. Int. J. Fuzzy Syst. 25, 3177–3192 (2023). https://doi.org/10.1007/s40815-023-01563-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-023-01563-5

Keywords

Search

Navigation