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Fault estimation and fault-tolerant control for linear discrete time-varying stochastic systems

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  • Special Focus on Control and Analysis for Stochastic Systems
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Abstract

This paper presents a scheme for simultaneous fault estimation and fault-tolerant control of linear discrete time-varying stochastic systems. An observer is proposed to estimate the system state and the fault simultaneously. The estimation errors of both the system state and fault can achieve exponential stability in mean square sense even if the fault arbitrarily changes or is unbounded. The controllers of the drift term and diffusion term are designed separately, and then based on the estimated fault, the fault compensation is performed to realize fault tolerance. For the parameter design in the estimator and controllers, we provide two different algorithms via the cone complementarity linearization and the state transition matrix methods, respectively. As an extension, a class of quasi-linear systems is also discussed. A simulation example with two different fault types and an application in electromechanical servo systems are provided to illustrate the usefulness of the proposed scheme.

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References

  1. Ding S X. Model-based Fault Diagnosis Techniques. Berlin: Springer Science & Business Media, 2008

    Google Scholar 

  2. Du D, Jiang B, Shi P. Fault Tolerant Control for Switched Linear Systems. Berlin: Springer, 2015

    Book  MATH  Google Scholar 

  3. Sun S, Zhang H, Zhang J, et al. Fault estimation and tolerant control for discrete-time multiple delayed fuzzy stochastic systems with intermittent sensor and actuator faults. IEEE Trans Cybern, 2020. doi: https://doi.org/10.1109/TCYB.2020.2965140

  4. Guo S, Jiang B, Zhu F, et al. Luenberger-like interval observer design for discrete-time descriptor linear system. Syst Control Lett, 2019, 126: 21–27

    Article  MathSciNet  MATH  Google Scholar 

  5. Yan X G, Edwards C. Nonlinear robust fault reconstruction and estimation using a sliding mode observer. Automatica, 2007, 43: 1605–1614

    Article  MathSciNet  MATH  Google Scholar 

  6. Yang H, Yin S. Reduced-order sliding-mode-observer-based fault estimation for Markov jump systems. IEEE Trans Automat Contr, 2019, 64: 4733–4740

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhao D, Li Y, Ahn C K, et al. Optimal state and fault estimation for two-dimensional discrete systems. Automatica, 2020, 115: 108856

    Article  MathSciNet  MATH  Google Scholar 

  8. Chen B S, Wang Y C. Synthetic Gene Network Modeling, Analysis, and Robust Design Methods. Boca Raton: CRC Press, 2014

    MATH  Google Scholar 

  9. Jiang X S, Tian S P, Zhang W H. pth moment exponential stability of general nonlinear discrete-time stochastic systems. Sci China Inf Sci, 2021, 64: 209204

    Article  Google Scholar 

  10. Shen M X, Fei C, Fei W Y, et al. Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays. Sci China Inf Sci, 2019, 62: 202205

    Article  MathSciNet  Google Scholar 

  11. Xiong X L, Yang X S, Cao J D, et al. Finite-time control for a class of hybrid systems via quantized intermittent control. Sci China Inf Sci, 2020, 63: 192201

    Article  MathSciNet  Google Scholar 

  12. Zhang T L, Deng F Q, Zhang W H. Study on stability in probability of general discrete-time stochastic systems. Sci China Inf Sci, 2020, 63: 159205

    Article  MathSciNet  Google Scholar 

  13. Jiang M M, Xie X J. State feedback stabilization of stochastic nonlinear time-delay systems: a dynamic gain method. Sci China Inf Sci, 2021, 64: 119202

    Article  MathSciNet  Google Scholar 

  14. Jiang X S, Tian S P, Zhang W H, et al. Pareto-optimal strategy for linear mean-field stochastic systems with constraint. IEEE Trans Cybern, 2020. doi: https://doi.org/10.1109/TCYB.2020.3023932

  15. Li Y, Zhang W, Liu X K. H index for discrete-time stochastic systems with Markovian jump and multiplicative noise. Automatica, 2018, 90: 286–293

    Article  MathSciNet  MATH  Google Scholar 

  16. Li X, Ahn C K, Lu D, et al. Robust simultaneous fault estimation and nonfragile output feedback fault-tolerant control for Markovian jump systems. IEEE Trans Syst Man Cybern Syst, 2019, 49: 1769–1776

    Article  Google Scholar 

  17. Su X, Shi P, Wu L, et al. Fault detection filtering for nonlinear switched stochastic systems. IEEE Trans Automat Contr, 2016, 61: 1310–1315

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang T, Deng F, Zhang W, et al. Fault detection filtering for Itô-type affine nonlinear stochastic systems. Asian J Control, 2021, 23: 620–635

    Article  MathSciNet  Google Scholar 

  19. Lin X, Zhang T, Zhang W, et al. New approach to general nonlinear discrete-time stochastic H control. IEEE Trans Automat Contr, 2019, 64: 1472–1486

    Article  MathSciNet  MATH  Google Scholar 

  20. LaSalle J P. The Stability of Dynamical Systems. Philadelphia: SIAM, 1976

    Book  MATH  Google Scholar 

  21. Zhang T, Deng F, Zhang W. Finite-time stability and stabilization of linear discrete time-varying stochastic systems. J Franklin Institute, 2019, 356: 1247–1267

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhang T, Deng F, Zhang W. Robust filtering for nonlinear discrete-time stochastic systems. Automatica, 2021, 123: 109343

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhang W, Zheng W X, Chen B S. Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise. Int J Control, 2017, 90: 2490–2507

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang Z H, Rodrigues M, Theilliol D, et al. Sensor fault estimation filter design for discrete-time linear time-varying systems. Acta Automatica Sin, 2014, 40: 2364–2369

    Article  Google Scholar 

  25. Yong S Z, Zhu M, Frazzoli E. A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems. Automatica, 2016, 63: 321–329

    Article  MathSciNet  MATH  Google Scholar 

  26. Li X, Liu H H T. Characterization of H index for linear time-varying systems. Automatica, 2013, 49: 1449–1457

    Article  MathSciNet  MATH  Google Scholar 

  27. Mao X. Stochastic Differential Equations and Applications. 2nd ed. Chichester: Horwood Publishing, 2007

    MATH  Google Scholar 

  28. Zhang B, Lim C C, Shi P, et al. Stabilization of a class of nonlinear systems with random disturbance via intermittent stochastic noise. IEEE Trans Automat Contr, 2020, 65: 1318–1324

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhang W, Xie L, Chen B S. Stochastic H2/H Control: A Nash Game Approach. Los Angeles: CRC Press, 2017

    Book  Google Scholar 

  30. Rami M A, Chen X, Zhou X Y. Discrete-time indefinite LQ control with state and control dependent noises. J Glob Optimization, 2002, 23: 245–265

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhu J W, Yang G H. Fault-tolerant control for linear systems with multiple faults and disturbances based on augmented intermediate estimator. IET Control Theor & Appl, 2017, 11: 164–172

    Article  MathSciNet  Google Scholar 

  32. El Ghaoui L, Oustry F, AitRami M. A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans Automat Contr, 1997, 42: 1171–1176

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhou B, Zhao T. On asymptotic stability of discrete-time linear time-varying systems. IEEE Trans Automat Contr, 2017, 62: 4274–4281

    Article  MathSciNet  MATH  Google Scholar 

  34. Mu Y, Zhang H, Xi R, et al. State and fault estimations for discrete-time T-S fuzzy systems with sensor and actuator faults. IEEE Trans Circuits Syst II, 2021. doi: https://doi.org/10.1109/TCSII.2021.3067708

  35. Liu X, Gao Z, Chan C C. Fault reconstruction and resilient control for discrete-time stochastic systems. ISA Trans, 2021. doi: https://doi.org/10.1016/j.isatra.2021.02.007

  36. Jiang X, Tian S, Zhang T, et al. Stability and stabilization of nonlinear discrete-time stochastic systems. Int J Robust Nonlin Control, 2019, 29: 6419–6437

    Article  MathSciNet  MATH  Google Scholar 

  37. Lu N, Sun X, Zheng X, et al. Command filtered adaptive fuzzy backstepping fault-tolerant control against actuator fault. ICIC Express Lett, 2021, 15: 357–365

    Google Scholar 

  38. Zheng X, Shen Q, Sun X, et al. Adaptive fault tolerant control for a class of high-order nonlinear systems. ICIC Express Lett, 2020, 14: 861–866

    Google Scholar 

  39. Zhang Z, Yang P, Hu X, et al. Sliding mode prediction fault-tolerant control of a quad-rotor system with multi-delays based on ICOA. Int J Innovative Comput Inform Control, 2021, 17: 49–65

    Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 62073144, 61733008, 61873099, 61803108), National Science Foundation of Guangdong Province (Grant No. 2020A1515010441), and Guangzhou Science and Technology Planning Project (Grant Nos. 202002030158, 202002030389), Key-area Research and Development Program of Guangdong Province (Grant No. 2020B0909020001), Science and Technology Research Project of Chongqing Education Commission (Grant Nos. KJZD-M201900801, KJQN201900831), and Chongqing Natural Science Foundation (Grant No. cstc2020jcyj-msxmX0077).

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Correspondence to Feiqi Deng.

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Zhang, T., Deng, F., Sun, Y. et al. Fault estimation and fault-tolerant control for linear discrete time-varying stochastic systems. Sci. China Inf. Sci. 64, 200201 (2021). https://doi.org/10.1007/s11432-021-3280-4

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  • DOI: https://doi.org/10.1007/s11432-021-3280-4

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