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Fault Detection for Complex Systems with Channel Fadings, Randomly Occurring Multiple Delays and Infinitely Distributed Delays

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Abstract

This paper is concerned with the fault detection (FD) problem for a class of discrete-time stochastic systems with channel fadings, randomly occurring multiple communication delays, and infinitely distributed delays. All of the three phenomena have the characteristics of randomly occurring and three sequences of stochastic variables which are mutually independent but obey the Bernoulli distribution are employed to describe them. The aim of this paper is to design an FD filter such that the FD dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Intensive analysis is utilized to derive the sufficient conditions for the designed FD filter, which guarantees the exponential stability and the prescribed H∞ performance. FD filter parameters are obtained by solving a convex optimization problem. An illustrative example is provided to demonstrate the effectiveness of the FD design scheme.

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References

  1. Wu L, Yao X, and Zheng W, Generalized H2 fault detection for Markovian jumping twodimensional systems, Automatica, 2012, 48(8): 1741–1750.

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhong G and Yang G, Fault detection for discrete-time switched systems in finite-frequency somain, Circuits Systems and Signal Processing, 2015, 34(4): 1305–1324.

    Article  MathSciNet  Google Scholar 

  3. Wang Y, Ding S, Ye H, et al., A new fault detection scheme for networked control systems subject to uncertain time-varying delay, IEEE Transactions on Signal Processing, 2008, 56(10): 2558–2568.

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Gao H, Meng X, and Chen T, Stabilization of networked control systems with a new delay characterization, IEEE Transactions on Automatic Control, 2008, 53(9): 2142–2148.

    Article  MathSciNet  MATH  Google Scholar 

  6. Hu S and Yue D, Event-triggered control design of linear networked systems with quantizations, Circuits Systems and Signal Processing, 2012, 51(1): 153–162.

    Google Scholar 

  7. Che W, Wang J, and Yang G, Quantized H ∞ filtering for networked systems with random sensor packet losses, IET Control Theory Appl, 2010, 4(8): 1339–1352.

    Article  MathSciNet  Google Scholar 

  8. Fang H, Ye H, and Zhong M, Fault diagnosis of networked control systems, Annual Reviews in Control, 2007, 31(1): 55–68.

    Article  Google Scholar 

  9. Wang Z, Shen B, Dong H, et al., Networked systems with incomplete information, Abstract and Applied Analysis, 2015, Article ID 852103, 4 pages.

    Google Scholar 

  10. He X, Wang Z, Wang X, et al., Networked strong tracking filtering with multiple packet dropouts: Algorithms and applications, IEEE Transactions on Industrial Electronics, 2014, 61(3): 1454–1463.

    Article  Google Scholar 

  11. He X, Wang Z, Qin L, et al., Active fault tolerant control for an Internet-based networked threetank system, IEEE Transactions on Control Systems Technology, 2016, 24(6): 2150–2157.

    Article  Google Scholar 

  12. Hou N, Dong H, Wang Z, et al., Non-fragile state estimation for discrete Markovian jumping neural networks, Neurocomputing, 2016, 179: 238–245.

    Article  Google Scholar 

  13. Hou N, Dong H, Wang Z, et al., H ∞ state estimation for discrete-time neural networks with dis tributed delays and randomly occurring uncertainties through fading channels, Neural Networks, 2017, 89: 61–73.

    Article  Google Scholar 

  14. Ren W, Hou N, Wang Q, et al., Non-fragile H ∞ filtering for nonlinear systems with randomly occurring gain variations and channel fadings, Neurocomputing, 2015, 156: 176–185.

    Article  Google Scholar 

  15. Rappaport T, Wireless Communications: Principles and Practice, 2nd Edition, Prentice Hall, New Jersey, 2002.

    MATH  Google Scholar 

  16. Berry R and Gallager R, Communication over fading channels with delay constraints, IEEE Transactions on Information Theory, 2002, 48(5): 1135–1149.

    Article  MathSciNet  MATH  Google Scholar 

  17. Elia N, Remote stabilization over fading channels, Systems and Control Letters, 2005, 54(3): 237–249.

    Article  MathSciNet  MATH  Google Scholar 

  18. Xiao N, Xie L, and Qiu L, Feedback stabilization of discrete-time networked systems over fading channels, IEEE Transactions on Automatic Control, 2012, 57(9): 2176–2189.

    Article  MathSciNet  MATH  Google Scholar 

  19. Mostofi Y and Murray R, To drop or not to drop: Design principles for Kalman filtering over wireless fading channels, IEEE Transactions on Automatic Control, 2010, 54(2): 376–381.

    Article  MathSciNet  MATH  Google Scholar 

  20. Baillieul J and Antsaklis P, Control and communication challenges in networked real-time systems, Proceedings of the IEEE, 2007, 95(1): 9–28.

    Article  Google Scholar 

  21. Shen B, Wang Z, Shu H, et al., Robust H ∞ finite-horizon filtering with randomly occurred nonlinearities and quantization effects, Automatica, 2010, 46(11): 1743–1751.

    Article  MathSciNet  MATH  Google Scholar 

  22. Gao H and Chen T, H ∞ estimation for uncertain systems with limited communication capacity, IEEE Transactions on Automatic Control, 2007, 52(11): 2070–2084.

    Article  MathSciNet  MATH  Google Scholar 

  23. Dong H, Wang Z, and Gao H, Robust H ∞ filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts, IEEE Transactions on Signal Processing, 2010, 58(4): 1957–1966.

    Article  MathSciNet  Google Scholar 

  24. Liu Y, Wang Z, Liang J, et al., Synchronization and state estimation for discrete-time complex networks with distributed delays, IEEE Transactions on Systems, Man, and Cybernetics: Cybernetics, 2008, 38(5): 1314–1325.

    Article  Google Scholar 

  25. Dong H, Wang Z, Lam J, et al., Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2012, 42(2): 365–376.

    Article  Google Scholar 

  26. Li Z, Wang Z, Ding D, et al., Non-fragile H ∞ control with randomly occurring gain variations, distributed delays and channel fadings, IET Control Theory and Applications, 2015, 9(2): 222–231.

    Article  Google Scholar 

  27. Boyd S, Ghaoui L, Feron E, et al., Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA, SIAM, 1994.

    Book  MATH  Google Scholar 

  28. Wang Z, Ho D, Liu Y, et al., Robust H ∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements, Automatica, 2009, 45(3): 684–691.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Daqing Normal University, Daqing, 163712, China

    Yanqin Wang

  2. College of Electrical and Information Engineering, Northeast Petroleum University, Daqing, 163318, China

    Yanqin Wang & Weijian Ren

  3. College of Electrical and Information, Heilongjiang Bayi Agricultural University, Daqing, 163319, China

    Yang Lu

Authors
  1. Yanqin Wang
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  2. Weijian Ren
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  3. Yang Lu
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Corresponding author

Correspondence to Weijian Ren.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61422301 and 61374127, the Alexander von Humboldt Foundation of Germany and Youth Science Foundation of Daqing Normal University under Grant No. 11ZR10.

This paper was recommended for publication by Editor SUN Jian.

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Wang, Y., Ren, W. & Lu, Y. Fault Detection for Complex Systems with Channel Fadings, Randomly Occurring Multiple Delays and Infinitely Distributed Delays. J Syst Sci Complex 31, 419–435 (2018). https://doi.org/10.1007/s11424-017-6149-x

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  • DOI: https://doi.org/10.1007/s11424-017-6149-x

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