Circuits, Systems, and Signal Processing

, Volume 39, Issue 1, pp 111–137 | Cite as

Robust Fault Detection for Nonlinear Discrete Systems with Data Drift and Randomly Occurring Faults Under Weighted Try-Once-Discard Protocol

  • Weilu Chen
  • Jun HuEmail author
  • Xiaoyang Yu
  • Dongyan Chen
  • Junhua Du


This paper is concerned with the robust fault detection (FD) problem for discrete uncertain systems with data drift, randomly occurring faults (ROFs) and randomly occurring nonlinearities (RONs) under weighted try-once-discard (WTOD) protocol. The phenomena of the RONs are characterized by the Bernoulli distributed variable. The Markov chain with two states is introduced to describe the ROFs in the system. The data drift is depicted by an array of mutually independent stochastic variables with individual probabilistic distribution functions. Moreover, the WTOD protocol is utilized to lessen the incidence of data collisions and enhance the communication efficiency. An FD filter is established, and sufficient conditions are proposed under which the resultant filtering error system is stochastically stable and achieves a prescribed \(H_{\infty }\) performance irrespective of the simultaneous presence of the WTOD protocol mechanism, ROFs, RONs and data drift. Besides, the form of the desired filter parameters is presented in terms of the solutions to certain matrix inequalities. Finally, two examples are exploited to demonstrate the feasibility of the obtained robust FD algorithm.


Discrete nonlinear system Randomly occurring faults Data drift Weighted try-once-discard protocol Fault detection 


Compliance with Ethical Standards

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.


  1. 1.
    L. Cao, Q. Zhou, G. Dong, H. Li, Observer-based adaptive event-triggered control for nonstrict-feedback nonlinear systems with output constraint and actuator failures. IEEE Trans. Syst. Man Cybern. Syst. (2019). CrossRefGoogle Scholar
  2. 2.
    W. Chen, J. Hu, X. Yu, D. Chen, Protocol-based fault detection for discrete delayed systems with missing measurements: the uncertain missing probability case. IEEE Access 6, 76616–76626 (2018)CrossRefGoogle Scholar
  3. 3.
    Y. Chen, Z. Wang, W. Qian, F.E. Alsaadi, Finite-horizon \(H_{\infty }\) filtering for switched time-varying stochastic systems with random sensor nonlinearities and packet dropouts. Signal Process. 138, 138–145 (2017)CrossRefGoogle Scholar
  4. 4.
    Y. Chen, Z. Wang, B. Shen, H. Dong, Exponential synchronization for delayed dynamical networks via intermittent control: dealing with actuator saturations. IEEE Trans. Neural Netw. Learn. Syst. 30(4), 1000–1012 (2019)MathSciNetCrossRefGoogle Scholar
  5. 5.
    H. Dong, N. Hou, Z. Wang, H. Liu, Finite-horizon fault estimation under imperfect measurements and stochastic communication protocol: dealing with finite-time boundedness. Int. J. Robust Nonlinear Control 29(1), 117–134 (2019)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    H. Dong, Z. Wang, S.X. Ding, H. Gao, On \(H_{\infty }\) estimation of randomly occurring faults for a class of nonlinear time-varying systems with fading channels. IEEE Trans. Autom. Control 61(2), 479–484 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 8.
    H. Gao, T. Chen, L. Wang, Robust fault detection with missing measurements. Int. J. Control 81(5), 804–819 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    X. He, Z. Wang, Y.D. Ji, D. Zhou, Fault detection for discrete-time systems in a networked environment. Int. J. Syst. Sci. 41(8), 937–945 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    J. Hu, D. Chen, J. Du, State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays. Int. J. General Syst. 43(3–4), 387–401 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    J. Hu, Z. Wang, F.E. Alsaadi, T. Hayat, Event-based filtering for time-varying nonlinear systems subject to multiple missing measurements with uncertain missing probabilities. Inf. Fusion 38, 74–83 (2017)CrossRefGoogle Scholar
  12. 12.
    J. Hu, Z. Wang, H. Gao, Joint state and fault estimation for uncertain time-varying nonlinear systems with randomly occurring faults and sensor saturations. Automatica 97, 150–160 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    J. Hu, Z. Wang, S. Liu, H. Gao, A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements. Automatica 64, 155–162 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    J. Hu, H. Zhang, X. Yu, H. Liu, D. Chen, Design of sliding-mode-based control for nonlinear systems with mixed-delays and packet losses under uncertain missing probability. IEEE Trans. Syst. Man Cybern. Syst. (2019). CrossRefGoogle Scholar
  15. 15.
    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)MathSciNetCrossRefGoogle Scholar
  16. 16.
    B. Khaldi, F. Harrou, F. Cherif, Y. Sun, Monitoring a robot swarm using a data-driven fault detection approach. Robot. Auton. Syst. 97, 193–203 (2017)CrossRefGoogle Scholar
  17. 17.
    X. Li, H. Dong, Z. Wang, F. Han, Set-membership filtering for state-saturated systems with mixed time-delays under weighted try-once-discard protocol. IEEE Trans. Circuits Syst. II Express Briefs 66(2), 312–316 (2019)CrossRefGoogle Scholar
  18. 18.
    H. Li, Y. Gao, P. Shi, H.K. Lam, Observer-based fault detection for nonlinear systems with sensor fault and limited communication capacity. IEEE Trans. Autom. Control 61(9), 2745–2751 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    H. Liang, Z. Zhang, C.K. Ahn, Event-triggered fault detection and isolation of discrete-time systems based on geometric technique. IEEE Trans. Circuits Syst. II Express Briefs (2019). CrossRefGoogle Scholar
  20. 20.
    H. Liang, Y. Zhang, T. Huang, H. Ma, Prescribed performance cooperative control for multiagent systems with input quantization. IEEE Trans. Cybern. (2019). CrossRefGoogle Scholar
  21. 21.
    H. Liang, L. Zhang, H.R. Karimi, Q. Zhou, Fault estimation for a class of nonlinear semi-Markovian jump systems with partly unknown transition rates and output quantization. Int. J. Robust Nonlinear Control 28(18), 5962–5980 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    L. Liu, Y. Wang, L. Ma, J. Zhang, Y. Bo, Robust finite-horizon filtering for nonlinear time-delay Markovian jump systems with weighted try-once-discard protocol. Syst. Sci. Control Eng. 6(1), 180–194 (2018)CrossRefGoogle Scholar
  23. 23.
    J. Liu, D. Yue, Event-based fault detection for networked systems with communication delay and nonlinear perturbation. J. Frankl. Inst. 350(9), 2791–2807 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    H. Ma, H. Li, H. Liang, G. Dong, Adaptive fuzzy event-triggered control for stochastic nonlinear systems with full state constraints and actuator faults. IEEE Trans. Fuzzy Syst. (2019). CrossRefGoogle Scholar
  25. 25.
    M. Meng, J. Lam, J. Feng, K.C. Cheung, Stability and stabilization of boolean networks with stochastic delays. IEEE Trans. Autom. Control 64(2), 790–796 (2019)MathSciNetzbMATHGoogle Scholar
  26. 26.
    B. Shen, S .X. Ding, Z. Wang, Finite-horizon \(H_{\infty }\) fault estimation for uncertain linear discrete time-varying systems with known inputs. IEEE Trans. Circuits Syst. II Express Briefs 60(12), 902–906 (2013)CrossRefGoogle Scholar
  27. 27.
    Y. Tan, D. Du, S. Fei, Co-design of event generator and quantized fault detection for time-delayed networked systems with sensor saturations. J. Frankl. Inst. 354(15), 6914–6937 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    E. Tian, Z. Wang, L. Zou, D. Yue, Probabilistic-constrained filtering for a class of nonlinear systems with improved static event-triggered communication. Int. J. Robust Nonlinear Control 29(5), 1484–1498 (2019)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    E. Tian, W.K. Wong, D. Yue, T.C. Yang, \(H_{\infty }\) filtering for discrete-time switched systems with known sojourn probabilities. IEEE Trans. Autom. Control 60(9), 2446–2451 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    X. Wan, Z. Wang, M. Wu, X. Liu, State estimation for discrete time-delayed genetic regulatory networks with stochastic noises under the round-robin protocols. IEEE Trans. Nanobiosci 17(2), 145–154 (2018)CrossRefGoogle Scholar
  31. 31.
    G. Wang, M. Liu, Fault detection for discrete-time systems with fault signal happening randomly: the Markov approach. IEEE Access 5, 14680–14689 (2017)CrossRefGoogle Scholar
  32. 32.
    Z. Wang, Y. Wang, Y. Liu, Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays. IEEE Trans. Neural Netw. 21(1), 11–25 (2010)CrossRefGoogle Scholar
  33. 33.
    D. Wang, Z. Wang, B. Shen, Q. Li, \(H_{\infty }\) finite-horizon filtering for complex networks with state saturations: the weighted try-once-discard protocol. Int. J. Robust Nonlinear Control 29(7), 2096–2111 (2019)MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Y. Wang, S. Zhang, Y. Li, Fault detection for a class of non-linear networked control systems with data drift. IET Signal Process. 9(2), 120–129 (2015)CrossRefGoogle Scholar
  35. 35.
    Y. Wang, S. Zhang, Z. Li, M. Zhang, Fault detection for a class of nonlinear singular systems over networks with mode-dependent time delays. Circuits Syst. Signal Process. 33(10), 3085–3106 (2014)MathSciNetCrossRefGoogle Scholar
  36. 36.
    R. Yang, W.X. Zheng, \(H_{\infty }\) filtering for discrete-time 2-D switched systems: an extended average dwell time approach. Automatica 98, 302–313 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  37. 37.
    H. Zhang, J. Hu, H. Liu, X. Yu, F. Liu, Recursive state estimation for time-varying complex networks subject to missing measurements and stochastic inner coupling under random access protocol. Neurocomputing 346, 48–57 (2019)CrossRefGoogle Scholar
  38. 38.
    L. Zhang, H. Liang, Y. Sun, C.K. Ahn, Adaptive event-triggered fault detection for semi-Markovian jump systems with output quantization. IEEE Trans. Syst. Man Cybern. Syst. (2019). CrossRefGoogle Scholar
  39. 39.
    Z. Zhang, H. Liang, C. Wu, C.K. Ahn, Adaptive event-triggered output feedback fuzzy control for nonlinear networked systems with packet dropouts and random actuator failure. IEEE Trans. Fuzzy Syst. (2019). CrossRefGoogle Scholar
  40. 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)MathSciNetCrossRefGoogle Scholar
  41. 41.
    L. Zou, Z. Wang, H. Gao, Set-membership filtering for time-varying systems with mixed time-delays under round-robin and weighted try-once-discard protocols. Automatica 74, 341–348 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    L. Zou, Z. Wang, H. Gao, F.E. Alsaadi, Finite-horizon \(H_{\infty }\) consensus control of time-varying multi-agent systems with stochastic communication protocol. IEEE. Trans. Cybern. 47(8), 1830–1840 (2017)CrossRefGoogle Scholar
  43. 43.
    L. Zou, Z. Wang, Q.L. Han, D. Zhou, Ultimate boundedness control for networked systems with try-once-discard protocol and uniform quantization effects. IEEE Trans. Autom. Control 62(12), 6582–6588 (2017)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.The Higher Educational Key Laboratory for Measuring & Control Technology and Instrumentations of Heilongjiang ProvinceHarbin University of Science and TechnologyHarbinChina
  2. 2.School of ScienceHarbin University of Science and TechnologyHarbinChina
  3. 3.School of EngineeringUniversity of South WalesPontypriddUK
  4. 4.Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex SystemsHarbin University of Science and TechnologyHarbinChina
  5. 5.College of ScienceQiqihar UniversityQiqiharChina

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