A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 11 Issue 2
Feb.  2024

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 11.8, Top 4% (SCI Q1)
    CiteScore: 17.6, Top 3% (Q1)
    Google Scholar h5-index: 77, TOP 5
Turn off MathJax
Article Contents
Y. Zhu, N. Xu, F. Wu, X. Chen, and  D. Zhou,  “Fault estimation for a class of  Markov jump piecewise-affine systems: Current feedback based iterative learning approach,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 2, pp. 418–429, Feb. 2024. doi: 10.1109/JAS.2023.123990
Citation: Y. Zhu, N. Xu, F. Wu, X. Chen, and  D. Zhou,  “Fault estimation for a class of  Markov jump piecewise-affine systems: Current feedback based iterative learning approach,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 2, pp. 418–429, Feb. 2024. doi: 10.1109/JAS.2023.123990

Fault Estimation for a Class of  Markov Jump Piecewise-Affine Systems: Current Feedback Based Iterative Learning Approach

doi: 10.1109/JAS.2023.123990
Funds:  This work was supported in part by the National Natural Science Foundation of China (62222310, U1813201, 61973131, 62033008), the Research Fund for the Taishan Scholar Project of Shandong Province of China and the NSFSD (ZR2022ZD34), Japan Society for the Promotion of Science (21K04129), and Fujian Outstanding Youth Science Fund (2020J06022)
More Information
  • In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuous-time Markov jump piecewise-affine (PWA) systems against actuator and sensor faults. Firstly, a novel mode-dependent PWA iterative learning observer with current feedback is designed to estimate the system states and faults, simultaneously, which contains both the previous iteration information and the current feedback mechanism. The auxiliary feedback channel optimizes the response speed of the observer, therefore the estimation error would converge to zero rapidly. Then, sufficient conditions for stochastic stability with guaranteed

    \begin{document}$ H_{\infty}$\end{document}

    performance are demonstrated for the estimation error system, and the equivalence relations between the system information and the estimated information can be established via iterative accumulating representation. Finally, two illustrative examples containing a class of tunnel diode circuit systems are presented to fully demonstrate the effectiveness and superiority of the proposed iterative learning observer with current feedback.


  • loading
  • [1]
    L. Chen, P. Shi, and M. Liu, “Fault reconstruction for Markovian jump systems with iterative adaptive observer,” Automatica, vol. 105, pp. 254–263, Jul. 2019. doi: 10.1016/j.automatica.2019.03.008
    Y. Ju, D. Ding, X. He, Q.-L. Han, and G. Wei, “Consensus control of multi-agent systems using fault-estimation-in-the-loop: Dynamic event-triggered case,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 8, pp. 1440–1451, Aug. 2022. doi: 10.1109/JAS.2021.1004386
    M. Hashemi and C. P. Tan, “Integrated fault estimation and fault tolerant control for systems with generalized sector input nonlinearity,” Automatica, vol. 119, p. 109098, Sept. 2020. doi: 10.1016/j.automatica.2020.109098
    J. Lan, “Asymptotic estimation of state and faults for linear systems with unknown perturbations,” Automatica, vol. 118, p. 108955, Aug. 2020. doi: 10.1016/j.automatica.2020.108955
    E. Mousavinejad, X. Ge, Q.-L. Han, T. J. Lim, and L. Vlacic, “An ellipsoidal set-membership approach to distributed joint state and sensor fault estimation of autonomous ground vehicles,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1107–1118, Jun. 2021. doi: 10.1109/JAS.2021.1004015
    Y. Xu, H. Yang, B. Jiang, and M. M. Polycarpou, “Distributed optimal fault estimation and fault-tolerant control for interconnected systems: A stackelberg differential graphical game approach,” IEEE Trans. Automat. Control, vol. 67, no. 2, pp. 926–933, Feb. 2022. doi: 10.1109/TAC.2021.3074284
    J. Yang, Z. Ning, Y. Zhu, L. Zhang, and H. K. Lam, “Semi-Markov jump linear systems with bi-boundary sojourn time: Anti-modal-asynchrony control,” Automatica, vol. 140, p. 110270, Jun. 2022. doi: 10.1016/j.automatica.2022.110270
    Z. Zhang and X. He, “Fault detection and isolation for linear parameter-varying systems with time-delays: A geometric approach,” Sci. China Inf. Sci., vol. 66, no. 7, p. 172202, Jul. 2023. doi: 10.1007/s11432-022-3632-2
    Y. Tian, Y. Chai, L. Feng, and K. Zhang, “Fault estimator design based on an iterative-learning scheme according to the forgetting factor for nonlinear systems,” Sci. China Inf. Sci., vol. 66, no. 7, p. 179201, Jul. 2023. doi: 10.1007/s11432-021-3342-3
    K. Zhang, B. Jiang, and F. Chen, “Multiple-model-based diagnosis of multiple faults with high-speed train applications using second-level adaptation,” IEEE Trans. Ind. Electron., vol. 68, no. 7, pp. 6257–6266, Jul. 2021. doi: 10.1109/TIE.2020.2994867
    X. Liu, Z. Gao, and M. Z. Q. Chen, “Takagi-sugeno fuzzy model based fault estimation and signal compensation with application to wind turbines,” IEEE Trans. Ind. Electron., vol. 64, no. 7, pp. 5678–5689, Jul. 2017. doi: 10.1109/TIE.2017.2677327
    H. Yang and S. Yin, “Actuator and sensor fault estimation for time-delay Markov jump systems with application to wheeled mobile manipulators,” IEEE Trans. Ind. Inf., vol. 16, no. 5, pp. 3222–3232, May 2020. doi: 10.1109/TII.2019.2915668
    X. Liu, Z. Gao, and A. Zhang, “Observer-based fault estimation and tolerant control for stochastic Takagi-Sugeno fuzzy systems with Brownian parameter perturbations,” Automatica, vol. 102, pp. 137–149, Apr. 2019. doi: 10.1016/j.automatica.2018.12.031
    H. Li, H. Gao, P. Shi, and X. Zhao, “Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach,” Automatica, vol. 50, no. 7, pp. 1825–1834, Jul. 2014. doi: 10.1016/j.automatica.2014.04.006
    S. Yin, H. Yang, and O. Kaynak, “Sliding mode observer-based FTC for Markovian jump systems with actuator and sensor faults,” IEEE Trans. Automat. Control, vol. 62, no. 7, pp. 3551–3558, Jul. 2017. doi: 10.1109/TAC.2017.2669189
    J. H. Lee, K. S. Lee, and W. C. Kim, “Model-based iterative learning control with a quadratic criterion for time-varying linear systems,” Automatica, vol. 36, no. 5, pp. 641–657, May 2000. doi: 10.1016/S0005-1098(99)00194-6
    M. Zheng, F. Zhang, and X. Liang, “A systematic design framework for iterative learning control with current feedback,” IFAC J. Syst. Control, vol. 5, pp. 1–10, Sept. 2018. doi: 10.1016/j.ifacsc.2018.06.001
    J. Shi, X. He, and D. Zhou, “Iterative learning based estimation of periodically occurring faults,” IET Control Theory Appl., vol. 10, no. 2, pp. 244–251, Jan. 2016. doi: 10.1049/iet-cta.2015.0791
    L. Feng, S. Xu, Y. Chai, and K. Zhang, “Iterative learning scheme-based fault estimation design for nonlinear systems with varying trial lengths and specified constraints,” Int. J. Robust Nonlinear Control, vol. 28, no. 16, pp. 4850–4864, Nov. 2018. doi: 10.1002/rnc.4287
    L. Yao, J. Qin, H. Wang, and B. Jiang, “Design of new fault diagnosis and fault tolerant control scheme for non-Gaussian singular stochastic distribution systems,” Automatica, vol. 48, no. 9, pp. 2305–2313, Sept. 2012. doi: 10.1016/j.automatica.2012.06.036
    L. Chen, Y. Zhu, F. Wu, and Y. Zhao, “Fault estimation observer design for Markovian jump systems with nondifferentiable actuator and sensor failures,” IEEE Trans. Cybern., vol. 53, no. 6, pp. 3844–3858, Jun. 2023. doi: 10.1109/TCYB.2022.3169290
    L. Liu, L. Ma, J. Zhang, and Y. Bo, “Sliding mode control for nonlinear Markovian jump systems under denial-of-service attacks,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1638–1648, Nov. 2020. doi: 10.1109/JAS.2019.1911531
    S. Dong, Z.-G. Wu, H. Su, P. Shi, and H. R. Karimi, “Asynchronous control of continuous-time nonlinear Markov jump systems subject to strict dissipativity,” IEEE Trans. Automat. Control, vol. 64, no. 3, pp. 1250–1256, Mar. 2019. doi: 10.1109/TAC.2018.2846594
    S. Dong, Z.-G. Wu, P. Shi, H. Su, and T. Huang, “Quantized control of Markov jump nonlinear systems based on fuzzy hidden Markov model,” IEEE Trans. Cybern., vol. 49, no. 7, pp. 2420–2430, Jul. 2019. doi: 10.1109/TCYB.2018.2813279
    H. Li, P. Shi, and D. Yao, “Adaptive sliding-mode control of Markov jump nonlinear systems with actuator faults,” IEEE Trans. Automat. Control, vol. 62, no. 4, pp. 1933–1939, Apr. 2017. doi: 10.1109/TAC.2016.2588885
    G. Feng, “Stability analysis of piecewise discrete-time linear systems,” IEEE Trans. Automat. Control, vol. 47, no. 7, pp. 1108–1112, Jul. 2002. doi: 10.1109/TAC.2002.800666
    C. Li, X. Liao, and X. Yang, “Switch control for piecewise affine chaotic systems,” Chaos, vol. 16, no. 3, p. 033104, Sept. 2006. doi: 10.1063/1.2213676
    R. Iervolino, D. Tangredi, and F. Vasc, “Lyapunov stability for piecewise affine systems via cone-copositivity,” Automatica, vol. 81, pp. 22–29, Jul. 2017. doi: 10.1016/j.automatica.2017.03.011
    Z. Ning, B. Cai, R. Weng, and L. Zhang, “Nonsynchronized state estimation for fuzzy Markov jump affine systems with switching region partitions,” IEEE Trans. Cybern., vol. 52, no. 4, pp. 2430–2439, Apr. 2022. doi: 10.1109/TCYB.2020.3002938
    Z. Ning, L. Zhang, G. Feng, and A. Mesbah, “Observation for Markov jump piecewise-affine systems with admissible region-switching paths,” IEEE Trans. Automat. Control, vol. 66, no. 9, pp. 4319–4326, Sept. 2021. doi: 10.1109/TAC.2020.3030845
    N. Xu, Y. Zhu, X. Chen, and C. Y. Su, “Passivity-based adaptive fault-tolerant control for continuous-time Markov jump PWA systems with actuator faults,” Int. J. Robust Nonlinear Control, vol. 32, no. 4, pp. 2300–2312, Mar. 2022. doi: 10.1002/rnc.5947
    L. Zhang and E. K. Boukas, “Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities,” Automatica, vol. 45, no. 2, pp. 463–468, Feb. 2009. doi: 10.1016/j.automatica.2008.08.010
    H. Yang and S. Yin, “Descriptor observers design for Markov jump systems with simultaneous sensor and actuator faults,” IEEE Trans. Automat. Control, vol. 64, no. 8, pp. 3370–3377, Aug. 2019. doi: 10.1109/TAC.2018.2879765
    M. Kvasnica, P. Grieder, M. Baotić, and F. J. Christophersen, Multi-Parametric Toolbox (MPT). 2006.


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索


    Article Metrics

    Article views (166) PDF downloads(54) Cited by()


    • The presented Markov jump PWA system contains both the Markov jump linear system and the ordinary PWA system as two special cases. The mode-dependent PWA iterative learning observer is developed to estimate both the augmented state and the non-differentiable actuator fault. With the increase of iteration numbers, the estimation error can be reduced gradually, and finally both the system state and the fault information can be estimated accurately
    • To ameliorate the iteration law to estimate faults rapidly with the minimum number of iterations, the current feedback mechanism is introduced into the iterative process, so that the designed iterative law includes both the results of the previous iteration based on the measurement output and the feedback information of the current iteration, where the effect of fault estimation errors on current iteration can be reduced by the feedback mechanism effectively
    • The mode-dependent and region-dependent Lyapunov function is constructed to adapt the stochastic stability with guaranteed H∞ performance. The investigated estimation error system illustrates the variations of switching model, the PWA regions, and the iteration process under the current feedback. Furthermore, the iterative relations between the plant information and the estimated information can be obtained


    DownLoad:  Full-Size Img  PowerPoint