Skip to main content
SpringerLink
Log in

Annulus-Event-Based Finite-Time Fault Detection for Discrete-Time Nonlinear Systems with Probabilistic Interval Delay and Randomly Occurring Faults

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, the finite-time fault detection (FTFD) problem is investigated for a class of discrete-time nonlinear systems subject to the probabilistic interval time-varying delay and the randomly occurring faults (ROFs) under the annulus-event-based communication strategy (AEBCS). A Bernoulli stochastic variable is used to depict the probability interval time-varying delay phenomenon, where the time delay is bounded and its probability distributions can be observed. The phenomena of the ROFs are characterized by the Markov chain with two states. Furthermore, the AEBCS is applied to determine whether the measured signals can be transmitted to the filter or not. For the fault detection (FD) problem, we propose some sufficient conditions to ensure that the error dynamics system is finite-time stochastically stable with the specified \(H_{\infty }\) performance index. Meanwhile, the gains of the filter can be calculated via the feasible solution to certain linear matrix inequalities. In the end, two numerical examples are proposed to verify the effectiveness of newly proposed FTFD method via the AEBCS.

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
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. F. Amato, M. Ariola, P. Dorato, Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37(9), 1459–1463 (2001)

    Article  MATH  Google Scholar 

  2. M. Atitallah, M. Davoodi, N. Meskin, Event-triggered fault detection for networked control systems subject to packet dropout. Asian J. Control. 20(6), 2195–2206 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Benzaouia, Y. Eddoukali, Robust fault detection and control for continuous-time switched systems with average dwell time. Circuits Syst. Signal Process. 37, 2357–2373 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  4. W. Chen, J. Hu, X. Yu, D. Chen, Z. Wu, Annulus-event-based fault detection for state-saturated nonlinear systems with time-varying delays. J. Frankl. Inst.-Eng. Appl. Math. 358(15), 8061–8084 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Dong, N. Hou, Z. Wang, Fault estimation for complex networks with randomly varying topologies and stochastic inner couplings. Automatica 112, 108734 (2020). https://doi.org/10.1016/j.automatica.2019.108734

    Article  MathSciNet  MATH  Google Scholar 

  6. X. Dong, S. He, V. Stojanovic, Robust fault detection filter design for a class of discrete-time conic-type non-linear Markov jump systems with jump fault signals. IET Control Theory Appl. 14(14), 1912–1919 (2020)

    Article  MathSciNet  Google Scholar 

  7. H. Dong, Z. Wang, H. Gao, On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays. Signal Process. 92(4), 1117–1125 (2012)

    Article  Google Scholar 

  8. D. Ding, Z. Wang, Q. Han, A set-membership approach to event-triggered filtering for general nonlinear systems over sensor networks. IEEE Trans. Autom. Control 65(4), 1792–1799 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  9. H. Gao, T. Chen, L. Wang, Robust fault detection with missing measurements. Int. J. Control 81(5), 804–819 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. X. He, Z. Wang, D. Zhou, Robust fault detection for networked systems with communication delay and data missing. Automatica 45(11), 2634–2639 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Hokouhi-Nejad, A.R. Ghiasi, M.A. Badamchizadeh, Robust simultaneous finite-time control and fault detection for uncertain linear switched systems with time-varying delay. IET Control Theory Appl. 11(7), 1041–1052 (2017)

    Article  MathSciNet  Google Scholar 

  12. J. Hu, C. Jia, H. Liu, X. Yi, Y. Liu, A survey on state estimation of complex dynamical networks. Int. J. Syst. Sci. 52(16), 3351–3367 (2021)

    Article  MathSciNet  Google Scholar 

  13. J. Hu, Z. Wang, H. Gao, Joint state and fault estimation for time-varying nonlinear systems with randomly occurring faults and sensor saturations. Automatica 97, 150–160 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Hu, Z. Wang, G. Liu, C. Jia, J. Williams, Event-triggered recursive state estimation for dynamical networks under randomly switching topologies and multiple missing measurements. Automatica 115, 108908 (2020). https://doi.org/10.1016/j.automatica.2020.108908

    Article  MathSciNet  MATH  Google Scholar 

  15. L. Hu, Z. Wang, Q.-L. Han, X. Liu, State estimation under false data injection attacks: security analysis and system protection. Automatica 87, 176–183 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  16. Y. Ju, X. Tian, H. Liu, L. Ma, Fault detection of networked dynamical systems: a survey of trends and techniques. Int. J. Syst. Sci. 52(16), 3390–3409 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Hu, H. Zhang, H. Liu, X. Yu, A survey on sliding mode control for networked control systems. Int. J. Syst. Sci. 52(6), 1129–1147 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  18. Y. Ju, G. Wei, D. Ding, S. Liu, Finite-horizon fault estimation for time-varying systems with multiple fading measurements under torus-event-based protocols. Int. J. Robust Nonlinear Control 29(13), 4594–4608 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  19. M.G. Kazemi, M. Montazeri, Robust fault detection of uncertain Lipschitz nonlinear systems with simultaneous disturbance attenuation level and enhanced fault sensitivity and Lipschitz constant. Circuits Syst. Signal Process. 37(10), 4256–4278 (2018)

    Article  MathSciNet  Google Scholar 

  20. Q. Li, B. Shen, Z. Wang, F.E. Alsaadi, An event-triggered approach to distributed \(H_{\infty }\) state estimation for state-saturated systems with randomly occurring mixed delays. J. Frankl. Inst.-Eng. Appl. Math. 355(6), 3104–3121 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  21. T. Li, Z. Dai, G. Song, H. Du, Simultaneous disturbance estimation and fault reconstruction using probability density functions. Appl. Math. Comput. 362(1), 1–12 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  22. Y. Pan, G. Yang, Event-triggered fault detection filter design for nonlinear networked systems. IEEE Trans. Syst. Man Cybern. Syst. 48(11), 1851–1862 (2018)

    Article  Google Scholar 

  23. W. Ren, S. Sun, N. Hou, C. Kang, Event-triggered non-fragile \(H_{\infty }\) fault detection for discrete time-delayed nonlinear systems with channel fadings. J. Frankl. Inst.-Eng. Appl. Math. 355(1), 436–457 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  24. R. Sakthivel, V. Suveetha, V. Nithya, Finite-time fault detection filter design for complex systems with multiple stochastic communication and distributed delays. Chaos Solitons Fractals 136, 109778 (2020). https://doi.org/10.1016/j.chaos.2020.109778

    Article  MathSciNet  MATH  Google Scholar 

  25. D. Sauter, S. Li, C. Aubrun, Robust fault diagnosis of networked control systems. Int. J. Adapt. Control Signal Process. 23(8), 722–736 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. S. Song, J. Hu, D. Chen, W. Chen, Z. Wu, An event-triggered approach to robust fault detection for nonlinear uncertain Markovian jump systems with time-varying delays. Circuits Syst. Signal Process. 39(7), 3445–3469 (2020)

    Article  MATH  Google Scholar 

  27. W. Sun, Y. Liu, H. Gao, Constrained sampled-data ARC for a class of cascaded nonlinear systems with applications to Motor-Servo systems. IEEE Trans. Ind. Inform. 15(2), 766–776 (2019)

    Article  Google Scholar 

  28. W. Sun, H. Pan, J. Yu, H. Gao, Reliability control for uncertain half-car active suspension systems with possible actuator faults. IET Control Theory Appl. 8(9), 746–754 (2014)

    Article  MathSciNet  Google Scholar 

  29. X. Wang, G. Yang, Event-based fault detection for non-linear networked systems with multi-data transmission and output quantisation. IET Control Theory Appl. 11(16), 2698–2706 (2017)

    Article  MathSciNet  Google Scholar 

  30. Y. Wang, S. Ding, H. Ye, G. Wang, A new fault detection scheme for networked control systems subject to uncertain time-varying delay. IEEE Trans. Signal Process. 56(10), 5258–5268 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  31. Y. Wang, P. Shi, C. Lim, Y. Liu, Event-triggered fault detection filter design for a continuous-time networked control system. IEEE Trans. Cybern. 46(12), 3414–3426 (2016)

    Article  Google Scholar 

  32. Z. Wang, P. Shi, C. Lim, \(H_{-}/H_{\infty }\) fault detection observer in finite frequency domain for linear parameter-varying descriptor systems. Automatica 86, 38–45 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. M. Wang, Z. Wang, Y. Chen, W. Sheng, Event-based adaptive neural tracking control for discrete-time stochastic nonlinear systems: a triggering threshold compensation strategy. IEEE Trans. Neural Netw. Learn. Syst. 31(6), 1968–1981 (2020)

    Article  MathSciNet  Google Scholar 

  34. S. Xiao, Y. Zhang, B. Zhang, Event-triggered networked fault detection for positive Markovian systems. Signal Process. 157, 161–169 (2019)

    Article  Google Scholar 

  35. S. Xu, T. Chen, J. Lam, Robust \(H_{\infty }\) filtering for uncertain Markovian jump systems with mode-dependent time-delays. IEEE Trans. Autom. Control 48(5), 900–907 (2003)

    MATH  Google Scholar 

  36. Z. Yin, X. Jiang, F. Wang, Stability criteria for systems with multiple probabilistic intervals time-varying delay. Int. J. Control Autom Syst. 18(4), 877–885 (2020)

    Article  Google Scholar 

  37. D. Yue, Q. Han, Robust \(H_{\infty }\) filter design of uncertain descriptor systems with discrete and distributed delays. IEEE Trans. Signal Process. 52(11), 3200–3212 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  38. Y. Zhang, H. Fang, Y. Zheng, X. Li, Torus-event-based fault diagnosis for stochastic multirate time-varying systems with constrained fault. IEEE Trans. Cybern. 50(6), 2803–2813 (2020)

    Article  Google Scholar 

  39. Y. Zhang, Z. Wang, L. Ma, F.E. Alsaadi, Annulus-event-based fault detection. isolation and estimation for multirate time-varying systems: applications to a three-tank system. J. Process. Control 75, 48–58 (2019)

    Article  Google Scholar 

  40. Y. Zhang, Z. Wang, L. Zou, Z. Liu, Fault detection filter design for networked multi-rate systems with fading measurements and randomly occurring faults. IET Control Theory Appl. 10(5), 573–581 (2016)

    Article  MathSciNet  Google Scholar 

  41. Z. Zhao, Z. Wang, L. Zou, J. Guo, Set-membership filtering for time-varying complex networks with uniform quantisations over randomly delayed redundant channels. Int. J. Syst. Sci. 51(16), 3364–3377 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  42. Y. Zheng, H. Fang, H. Wang, Takagi-Sugeno fuzzy-model-based fault detection for networked control systems with Markov delays. IEEE Trans. Syst. Man Cybern. Part B-Cybern. 36(4), 924–929 (2006)

    Article  Google Scholar 

  43. L. Zou, Z. Wang, G. Hang, X. Liu, Set-membership filtering subject to impulsive measurement outliers: a recursive algorithm. IEEE/CAA J. Autom. Sinica 8(2), 377–388 (2021)

    Article  MathSciNet  Google Scholar 

  44. L. Zou, Z. Wang, Q. Han, D. Zhou, Moving horizon estimation for networked time-delay systems under Round-Robin protocol. IEEE Trans. Autom. Control. 64(12), 5191–5198 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  45. L. Zou, Z. Wang, Q. Han, D. Zhou, Recursive filtering for time-varying systems with random access protocol. IEEE Trans. Autom. Control. 64(2), 720–727 (2019)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Harbin University of Science and Technology, Harbin, 150080, China

    Zhihui Wu & Jun Hu

  2. Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, China

    Zhihui Wu, Bei Li, Jun Hu & Dongyan Chen

  3. Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex Systems, Harbin University of Science and Technology, Harbin, 150080, China

    Zhihui Wu, Bei Li, Jun Hu & Dongyan Chen

Authors
  1. Zhihui Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dongyan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhihui Wu.

Ethics declarations

Conflict of interest

The authors claim that there are no potential conflicts of interest. In addition, this submission has been approved by all co-authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported by the Natural Science Foundation of Heilongjiang Province of China under Grant YQ2020A004, the National Natural Science Foundation of China 12071102, and the Talent Training Project of Reform and Development Foundation for Local Universities from Central Government of China: Youth Talent Project.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, Z., Li, B., Hu, J. et al. Annulus-Event-Based Finite-Time Fault Detection for Discrete-Time Nonlinear Systems with Probabilistic Interval Delay and Randomly Occurring Faults. Circuits Syst Signal Process 41, 4818–4847 (2022). https://doi.org/10.1007/s00034-022-02019-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-022-02019-1

Keywords

Search

Navigation