International Journal of Fuzzy Systems

, Volume 21, Issue 2, pp 532–544 | Cite as

Event-Triggered State Estimation for T–S Fuzzy Neural Networks with Stochastic Cyber-Attacks

  • Jinliang LiuEmail author
  • Tingting Yin
  • Xiangpeng Xie
  • Engang Tian
  • Shumin Fei


This paper is mainly concerned with event-triggered state estimation for Takagi–Sugeno (T–S) fuzzy neural networks subjected to stochastic cyber-attacks. An event-triggered scheme is utilized to decide whether the sampled data should be delivered or not. By taking the influence of the cyber-attacks into consideration, a T–S fuzzy model for the state estimation of neural networks is established with the event-triggered scheme. Through the utilization of Lyapunov stability theory and linear matrix inequality (LMI) techniques, the sufficient conditions are derived which can ensure the stability of estimator error systems. In addition, the gains of the estimator are acquired in the form of LMIs. Finally, a simulated example is presented to illustrate the effectiveness of the proposed method.


Event-triggered scheme T–S fuzzy neural networks Stochastic cyber-attacks State estimation 


  1. 1.
    Tsai, C., Wu, H., Tai, F., Chen, Y.: Distributed consensus formation control with collision and obstacle avoidance for uncertain networked omnidirectional multi-robot systems using fuzzy wavelet neural networks. Int. J. Fuzzy Syst. 19(5), 1375–1391 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Niu, B., Wang, D., Alotaibi, N. D., Alsaadi, F. E.: Adaptive neural state-feedback tracking control of stochastic nonlinear switched systems: An average dwell-time method. IEEE Trans. Neural Netw. Learn. Syst. (2018).
  3. 3.
    Wang, Y., Chien, C., Chi, R., Hou, Z.: A fuzzy-neural adaptive terminal iterative learning control for fed-batch fermentation processes. Int. J. Fuzzy Syst. 17(3), 423–433 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Niu, B., Li, H., Zhang, Z., Li, J., Hayat, T., Alsaadi, F. E.: Adaptive neural-network-based dynamic surface control for stochastic interconnected nonlinear nonstrict-feedback systems with dead zone. IEEE Trans. Syst. Man Cybern. Syst. (2018).
  5. 5.
    Fan, D., Wang, Z., Wang, Q.: Optimal control of directional deep brain stimulation in the parkinsonian neuronal network. Commun. Nonlinear Sci. Numer. Simul. 36, 219–237 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Xu, Q., Yang, Y., Zhang, C., Zhang, L.: Deep convolutional neural network-based autonomous marine vehicle maneuver. Int. J. Fuzzy Syst. 20(2), 687–699 (2018)CrossRefGoogle Scholar
  7. 7.
    Xu, B., Liu, Q.: Iterative projection based sparse reconstruction for face recognition. Neurocomputing 284, 99–106 (2018)CrossRefGoogle Scholar
  8. 8.
    Zhao, J., Lin, C.: An interval-valued fuzzy cerebellar model neural network based on intuitionistic fuzzy sets. Int. J. Fuzzy Syst. 19(3), 881–894 (2017)CrossRefGoogle Scholar
  9. 9.
    Chang, J., Wang, R., Wang, W., Huang, C.: Implementation of an object-grasping robot arm using stereo vision measurement and fuzzy control. Int. J. Fuzzy Syst. 17(2), 193–205 (2015)CrossRefGoogle Scholar
  10. 10.
    Liu, J., Tang, J., Fei, S.: Event-triggered \({H_\infty }\) filter design for delayed neural network with quantization. Neural Netw. 82, 39–48 (2016)CrossRefGoogle Scholar
  11. 11.
    Lee, C., Lee, Y., Lin, C.: Nonlinear systems identification and control using uncertain rule-based fuzzy neural systems with stable learning mechanism. Int. J. Fuzzy Syst. 19(2), 470–488 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Xu, C., Zhang, Q., Wu, Y.: Existence and exponential stability of periodic solution to fuzzy cellular neural networks with distributed delays. Int. J. Fuzzy Syst. 18(1), 41–51 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Zheng, M., Li, L., Peng, H., Xiao, J., Yang, Y., Zhang, Y., Zhao, H.: Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks. Commun. Nonlinear Sci. Numer. Simul. 59, 272–291 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Liu, J., Wei, L., Xie, X., Yue, D.: Distributed event-triggered state estimators design for networked sensor systems with deception attacks. IET Control Theory Appl. (2018). Google Scholar
  15. 15.
    Juang, C., Hsieh, C.: A locally recurrent fuzzy neural network with support vector regression for dynamic-system modeling. IEEE Trans. Fuzzy Syst. 18(2), 261–273 (2010)Google Scholar
  16. 16.
    Liu, J., Xia, J., Tian, E., Fei, S.: Hybrid-driven-based \(H_\infty \) filter design for neural networks subject to deception attacks. Appl. Math. Comput. 320, 158–174 (2018)MathSciNetGoogle Scholar
  17. 17.
    Liu, Y., Wang, T., Chen, M., Shen, H., Wang, Y., Duan, D.: Dissipativity-based state estimation of delayed static neural networks. Neurocomputing 247, 137–143 (2017)CrossRefGoogle Scholar
  18. 18.
    Huang, H., Huang, T., Chen, X.: Reduced-order state estimation of delayed recurrent neural networks. Neural Netw. 98, 59–64 (2018)CrossRefGoogle Scholar
  19. 19.
    Liu, J., Xia, J., Cao, J., Tian, E.: Quantized state estimation for neural networks with cyber attacks and hybrid triggered communication scheme. Neurocomputing 291, 35–49 (2018)CrossRefGoogle Scholar
  20. 20.
    Liu, J., Wei, L., Cao, J., Fei, S.: Hybrid-driven \({H_\infty }\) filter design for T-S fuzzy systems with quantization. Nonlinear Anal. Hybrid Syst. 31, 135–152 (2019)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Chen, J., Xu, S., Ma, Q., Zhuang, G.: Relaxed stability conditions for discrete-time T–S fuzzy systems via double homogeneous polynomial approach. Int. J. Fuzzy Syst. 20(3), 741–749 (2018)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Qiao, L., Yang, Y.: Fault-tolerant control for T–S fuzzy systems with sensor faults: application to a ship propulsion system. J. Frankl. Inst. 355(12), 4854–4872 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Peng, C., Wen, L., Yang, J.: On delay-dependent robust stability criteria for uncertain T–S fuzzy systems with interval time-varying delay. Int. J. Fuzzy Syst. 13(1), 35–44 (2011)MathSciNetGoogle Scholar
  24. 24.
    Liang, H., Zhang, L., Karimi, H. R., Zhou, Q.: Fault estimation for a class of nonlinear semi-Markovian jump systems with partly unknown transition rates and output quantization. Int. J. Robust Nonlinear Control. (2018).
  25. 25.
    Zhang, Z., Zhou, Q., Wu, C., Li, H.: Dissipativity-based reliable interval type-2 fuzzy filter design for uncertain nonlinear systems. Int. J. Fuzzy Syst. 20(2), 390–402 (2018)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Zhang, Y., Tao, G., Chen, M., Wen, L.: Parameterization and adaptive control of multivariable noncanonical T–S fuzzy systems. IEEE Trans. Fuzzy Syst. 25(1), 156–171 (2017)CrossRefGoogle Scholar
  27. 27.
    Gao, M., Sheng, L., Zhou, D., Niu, Y.: Event-based fault detection for T–S fuzzy systems with packet dropouts and (x, v)-dependent noises. Signal Process. 138, 211–219 (2017)CrossRefGoogle Scholar
  28. 28.
    Xie, X., Yue, D., Zhu, X.: Further studies on control synthesis of discrete-time T–S fuzzy systems via augmented multi-indexed matrix approach. IEEE Trans. Cybern. 44(12), 2784–2791 (2014)CrossRefGoogle Scholar
  29. 29.
    Wu, X., Wang, Y., Dang, X.: Robust adaptive sliding-mode control of condenser-cleaning mobile manipulator using fuzzy wavelet neural network. Fuzzy Sets Syst. 235, 62–82 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Mohammadzadeh, A., Ghaemi, S., Kaynak, O., Khanmohammadi, S.: Robust \(H_\infty \)-based synchronization of the fractional-order chaotic systems by using new self-evolving nonsingleton type-2 fuzzy neural networks. IEEE Trans. Fuzzy Syst. 24(6), 1544–1554 (2016)CrossRefGoogle Scholar
  31. 31.
    Ali, M.S., Gunasekaran, N., Zhu, Q.: State estimation of T–S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control. Fuzzy Sets Syst. 306, 87–104 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Ali, M.S., Vadivel, R., Saravanakumar, R.: Design of robust reliable control for T–S fuzzy Markovian jumping delayed neutral type neural networks with probabilistic actuator faults and leakage delays: an event-triggered communication scheme. ISA Trans. 77, 30–48 (2018)CrossRefGoogle Scholar
  33. 33.
    Yue, D., Tian, E., Han, Q.: A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans. Autom. Control 58(2), 475–481 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Liu, J., Gu, Y., Xie, X., Yue, D., Park, J. H.: Hybrid-driven-based \(H_\infty \) control for networked cascade control systems with actuator saturations and stochastic cyber attacks. IEEE Trans. Syst. Man Cybern. Syst. (2018).
  35. 35.
    Liu, J., Gu, Y., Cao, J., Fei, S.: Distributed event-triggered \(H_\infty \) filtering over sensor networks with sensor saturations and cyber-attacks. ISA Trans. 81, 63–75 (2018)CrossRefGoogle Scholar
  36. 36.
    Choi, Y., Yoo, S.: Event-triggered decentralized adaptive fault-tolerant control of uncertain interconnected nonlinear systems with actuator failures. ISA Trans. 77, 77–89 (2018)CrossRefGoogle Scholar
  37. 37.
    Xie, X., 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. (2017).
  38. 38.
    Liu, J., Zha, L., Cao, J., Fei, S.: Hybrid-driven-based stabilisation for networked control systems. IET Control Theory Appl. 10(17), 2279–2285 (2016)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Liu, J., Wei, L., Tian, E., Fei, S., Cao, J.: \(H_\infty \) filtering for networked systems with hybrid-triggered communication mechanism and stochastic cyber attacks. J. Frankl. Inst. 354(18), 8490–8512 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Liu, J., Zha, L., Xie, X., Tian, E.: Resilient observer-based control for networked nonlinear T–S fuzzy systems with hybrid-triggered scheme. Nonlinear Dyn. 91(3), 2049–2061 (2018)CrossRefzbMATHGoogle Scholar
  41. 41.
    Chen, X., Wang, Y., Hu, S.: Event-based robust stabilization of uncertain networked control systems under quantization and denial-of-service attacks. Inf. Sci. 459, 369–386 (2018)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Peng, C., Li, J., Fei, M.: Resilient event-triggering \(H_\infty \) load frequency control for multi-area power systems with energy-limited dos attacks. IEEE Trans. Power Syst. 32(5), 4110–4118 (2017)CrossRefGoogle Scholar
  43. 43.
    Yang, W., Lei, L., Yang, C.: Event-based distributed state estimation under deception attack. Neurocomputing 270, 145–151 (2017)CrossRefGoogle Scholar
  44. 44.
    Ding, D., Wei, G., Zhang, S., Liu, Y., Alsaadi, F.E.: On scheduling of deception attacks for discrete-time networked systems equipped with attack detectors. Neurocomputing 219, 99–106 (2017)CrossRefGoogle Scholar
  45. 45.
    Peng, L., Cao, X., Shi, H., Sun, C.: Optimal jamming attack schedule for remote state estimation with two sensors. J. Frankl. Inst. (2018).
  46. 46.
    Liu, J., Wei, L., Xie, X., Tian, E., Fei, S.: Quantized stabilization for T–S fuzzy systems with hybrid-triggered mechanism and stochastic cyber-attacks. IEEE Trans. Fuzzy Syst. (2018).
  47. 47.
    Ding, D., Wang, Z., Ho, D.W., Wei, G.: Observer-based event-triggering consensus control for multiagent systems with lossy sensors and cyber-attacks. IEEE Trans. Cybern. 47(8), 1936–1947 (2017)CrossRefGoogle Scholar
  48. 48.
    Peng, C., Tian, E., Zhang, J., Du, D.: Decentralized event-triggering communication scheme for large-scale systems under network environments. Inf. Sci. 380, 132–144 (2017)CrossRefGoogle Scholar
  49. 49.
    Zha, L., Tian, E., Xie, X., Gu, Z., Cao, J.: Decentralized event-triggered \(H_\infty \) control for neural networks subject to cyber-attacks. Inf. Sci. 457–458, 141–155 (2018)MathSciNetCrossRefGoogle Scholar
  50. 50.
    Fridman, E., Shaked, U., Xie, L.: Robust \(H_\infty \) filtering of linear systems with time-varying delay. IEEE Trans. Autom. Control 48(1), 159–165 (2003)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Jinliang Liu
    • 1
    • 2
    Email author
  • Tingting Yin
    • 1
  • Xiangpeng Xie
    • 3
  • Engang Tian
    • 4
  • Shumin Fei
    • 5
  1. 1.College of Information EngineeringNanjing University of Finance and EconomicsNanjingChina
  2. 2.Key Laboratory of Grain Information Processing and ControlHenan University of Technology, Ministry of EducationHenanChina
  3. 3.Institute of Advanced TechnologyNanjing University of Posts and TelecommunicationsNanjingChina
  4. 4.School of Optical-Electrical and Computer EngineeringUniversity of Shanghai for Science and TechnologyShanghaiChina
  5. 5.School of AutomationSoutheast UniversityNanjingChina

Personalised recommendations