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SCIENCE CHINA Information Sciences, Volume 64 , Issue 10 : 200201(2021) https://doi.org/10.1007/s11432-021-3280-4

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

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  • ReceivedFeb 15, 2021
  • AcceptedMay 8, 2021
  • PublishedSep 14, 2021

Abstract


Acknowledgment

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).


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. Google Scholar

[3] Sun S, Zhang H, Zhang J. Fault Estimation and Tolerant Control for Discrete-Time Multiple Delayed Fuzzy Stochastic Systems With Intermittent Sensor and Actuator Faults.. IEEE Trans Cybern, 2020, : 1-13 CrossRef PubMed Google Scholar

[4] Guo S, Jiang B, Zhu F. Luenberger-like interval observer design for discrete-time descriptor linear system. Syst Control Lett, 2019, 126: 21-27 CrossRef Google Scholar

[5] Yan X G, Edwards C. Nonlinear robust fault reconstruction and estimation using a sliding mode observer. Automatica, 2007, 43: 1605-1614 CrossRef 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 CrossRef Google Scholar

[7] Zhao D, Li Y, Ahn C K. Optimal state and fault estimation for two-dimensional discrete systems. Automatica, 2020, 115: 108856 CrossRef Google Scholar

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

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

[10] Shen M, Fei C, Fei W. Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays. Sci China Inf Sci, 2019, 62: 202205 CrossRef Google Scholar

[11] Xiong X, Yang X, Cao J. Finite-time control for a class of hybrid systems via quantized intermittent control. Sci China Inf Sci, 2020, 63: 192201 CrossRef Google Scholar

[12] Zhang T, Deng F, Zhang W. Study on stability in probability of general discrete-time stochastic systems. Sci China Inf Sci, 2020, 63: 159205 CrossRef Google Scholar

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

[14] Jiang X, Tian S, Zhang W. Pareto-Optimal Strategy for Linear Mean-Field Stochastic Systems With H Constraint.. IEEE Trans Cybern, 2020, : 1-14 CrossRef PubMed Google Scholar

[15] Li Y, Zhang W, Liu X K. Automatica, 2018, 90: 286-293 CrossRef Google Scholar

[16] Li X, Ahn C K, Lu D. 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 CrossRef Google Scholar

[17] Su X, Shi P, Wu L. Fault Detection Filtering for Nonlinear Switched Stochastic Systems. IEEE Trans Automat Contr, 2016, 61: 1310-1315 CrossRef Google Scholar

[18] Zhang T, Deng F, Zhang W. Fault detection filtering for It??type affine nonlinear stochastic systems. Asian J Control, 2021, 23: 620-635 CrossRef Google Scholar

[19] Lin X, Zhang T, Zhang W. New Approach to General Nonlinear Discrete-Time Stochastic $H_\infty$ Control. IEEE Trans Automat Contr, 2019, 64: 1472-1486 CrossRef Google Scholar

[20] LaSalle J. P. The Stability of Dynamical Systems SIAM: Philadelphia, 1976. 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 CrossRef Google Scholar

[22] Zhang T, Deng F, Zhang W. Automatica, 2021, 123: 109343 CrossRef 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 CrossRef ADS Google Scholar

[24] Wang Z H, Rodrigues M, Theilliol D. Sensor Fault Estimation Filter Design for Discrete-time Linear Time-varying Systems. Acta Automatica Sin, 2014, 40: 2364-2369 CrossRef 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 CrossRef Google Scholar

[26] Li X, Liu H H T. Automatica, 2013, 49: 1449-1457 CrossRef Google Scholar

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

[28] Zhang B, Lim C C, Shi P. Stabilization of a Class of Nonlinear Systems With Random Disturbance via Intermittent Stochastic Noise. IEEE Trans Automat Contr, 2020, 65: 1318-1324 CrossRef Google Scholar

[29] Zhang W, Xie L, Chen B S. Stochastic $H_2/H_{\infty}$ Control: A Nash Game Approach. Los Angeles: CRC Press, 2017. Google Scholar

[30] Rami M A, Chen X, Zhou X Y. J glob Optimization, 2002, 23: 245-265 CrossRef 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 CrossRef 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 CrossRef 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 CrossRef Google Scholar

[34] Mu Y, Zhang H, Xi R. State and Fault Estimations for Discrete-Time T-S Fuzzy Systems with Sensor and Actuator Faults. IEEE Trans Circuits Syst II, 2021, : 1-1 CrossRef Google Scholar

[35] Liu X, Gao Z, Chan C C. Fault reconstruction and resilient control for discrete-time stochastic systems.. ISA Trans, 2021, 89 CrossRef PubMed Google Scholar

[36] Jiang X, Tian S, Zhang T. Stability and stabilization of nonlinear discrete?time stochastic systems. Int J Robust NOnlinear Control, 2019, 29: 6419-6437 CrossRef 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 Letters 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

  • Figure 1

    The diagram of the proposed fault-tolerant scheme.

  • Figure 4

    (Color online) The mean square values $E\|e_{x_k}\|^2$ and $E\|e_{f_k}\|^2$.

  • Figure 7

    (Color online) The state $x_k$ of system (1) under $\bar{f}_k$.

  •   

    Algorithm 1 A cone complementarity linearization algorithm

    Find a set of feasible solutions of LMI (2019filter1-ewdd)denoted by $\{P_{k,0}\}_{k\in~{\mathcal~N}_{T-1}}$,$\{X_{k,0}\}_{k\in~{\mathcal~N}_{T-1}}$;if there is none, the procedure exits. Set $i=0$.

    Solve the convex optimization problem to obtain $P_{k,i+1}$ and$X_{k,i+1}$: $$ \min_{X_{k,i+1},P_{k,i+1}} \sum_{k=0}^{T-1}\{\text{trace}({P}_{k,i}X_{k,i+1})+\text{trace}({X}_{k,i}P_{k,i+1})\} $$ subject to LMIs $$ \left[\begin{array}{ccc} -P_{k,i+1}&\bar{A}_k'&\bar{C}_k'\\ \bar{A}_k&-X_{k+1,i+1}&0\\ \bar{C}_k &0&-X_{k+1,i+1} \end{array}\right]<0, k\in {\mathcal N}_{T-1}, $$ and $$ \left[\begin{array}{cc} P_{k,i+1} & I \\ I & X_{k,i+1} \end{array}\right]\geq0, k\in {\mathcal N}_{T-1}. $$

    If a stopping criterion$|\sum_{k=0}^{T-1}\{\text{trace} ({P}_{k,i}X_{k,i+1})+\text{trace}({X}_{k,i}P_{k,i+1})\}-4nT|<\epsilon$ for a prescribed $\epsilon>0$ is satisfied,the procedure stops. Otherwise, set $i=i+1$and go back to step 2.

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