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Volume 9 Issue 6
Jun.  2022

IEEE/CAA Journal of Automatica Sinica

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J. Mao, X. Meng, and D. Ding, “Fuzzy set-membership filtering for discrete-time nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1026–1036, Jun. 2022. doi: 10.1109/JAS.2022.105416
Citation: J. Mao, X. Meng, and D. Ding, “Fuzzy set-membership filtering for discrete-time nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1026–1036, Jun. 2022. doi: 10.1109/JAS.2022.105416

Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

doi: 10.1109/JAS.2022.105416
Funds:  This work was supported in part by the National Natural Science Foundation of China (61973219, 61933007, 62073158), and the China Scholarship Council (201908310148)
More Information
  • In this article, the problem of state estimation is addressed for discrete-time nonlinear systems subject to additive unknown-but-bounded noises by using fuzzy set-membership filtering. First, an improved T-S fuzzy model is introduced to achieve highly accurate approximation via an affine model under each fuzzy rule. Then, compared to traditional prediction-based ones, two types of fuzzy set-membership filters are proposed to effectively improve filtering performance, where the structure of both filters consists of two parts: prediction and filtering. Under the locally Lipschitz continuous condition of membership functions, unknown membership values in the estimation error system can be treated as multiplicative noises with respect to the estimation error. Real-time recursive algorithms are given to find the minimal ellipsoid containing the true state. Finally, the proposed optimization approaches are validated via numerical simulations of a one-dimensional and a three-dimensional discrete-time nonlinear systems.


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  • [1]
    A. Ansari and D. S. Bernstein, “Input estimation for nonminimum-phase systems with application to acceleration estimation for a maneuvering vehicle,” IEEE Trans. Control Systems Technology, vol. 27, no. 4, pp. 1596–1607, 2019. doi: 10.1109/TCST.2018.2807798
    T. Knudsen and J. Leth, “A new continuous discrete unscented Kalman filter,” IEEE Trans. Autom. Control, vol. 64, no. 5, pp. 2198–2205, 2019. doi: 10.1109/TAC.2018.2867325
    R. Yildiz, M. Barut, and E. Zerdali, “A comprehensive comparison of extended and unscented Kalman filters for speed-sensorless control applications of induction motors,” IEEE Trans. Industrial Informatics, vol. 16, no. 10, pp. 6423–6432, 2020. doi: 10.1109/TII.2020.2964876
    D. Ding, Q.-L. Han, Z. Wang, and X. Ge, “Recursive filtering of distributed cyber-physical systems with attack detection,” IEEE Trans. Systems,Man,and Cybernetics: Systems, pp. 1–11, 2020.
    G. G. Koch, L. A. Maccari, R. C. L. F. Oliveira, and V. F. Montagner, “Robust $ \substack{{\cal{H}}_{\infty} } $ state feedback controllers based on linear matrix inequalities applied to grid-connected converters,” IEEE Trans. Industrial Electronics, vol. 66, no. 8, pp. 6021–6031, 2019. doi: 10.1109/TIE.2018.2870406
    J. Zhao and L. Mili, “A decentralized $ \substack{{\cal{H}}_{\infty} }$ unscented Kalman filter for dynamic state estimation against uncertainties,” IEEE Trans. Smart Grid, vol. 10, no. 5, pp. 4870–4880, 2019. doi: 10.1109/TSG.2018.2870327
    H. Gao, X. Meng, and T. Chen, “A parameter-dependent approach to robust $ \substack{{\cal{H}}_{\infty} }$ filtering for time-delay systems,” IEEE Trans. Autom. Control, vol. 53, no. 10, pp. 2420–2425, 2008. doi: 10.1109/TAC.2008.2007544
    L. Zou, Z. Wang, Q.-L. Han, and D. Zhou, “Moving horizon estimation of networked nonlinear systems with random access protocol,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 51, no. 5, pp. 2937–2948, 2021. doi: 10.1109/TSMC.2019.2918002
    Y. Zhao, X. He, J. Zhang, H. Ji, D. Zhou, and M. G. Pecht, “Detection of intermittent faults based on an optimally weighted moving average t2 control chart with stationary observations,” Automatica, vol. 123, Article No. 109298, 2021. doi: 10.1016/j.automatica.2020.109298
    C. Peng and H. Sun, “Switching-like event-triggered control for networked control systems under malicious denial of service attacks,” IEEE Trans. Autom. Control, vol. 65, no. 9, pp. 3943–3949, 2020. doi: 10.1109/TAC.2020.2989773
    F. Yang, N. Xia, and Q.-L. Han, “Event-based networked islanding detection for distributed solar PV generation systems,” IEEE Trans. Industrial Informatics, vol. 13, no. 1, pp. 322–329, 2017. doi: 10.1109/TII.2016.2607999
    A. Benavoli and D. Piga, “A probabilistic interpretation of setmembership filtering: Application to polynomial systems through polytopic bounding,” Automatica, vol. 70, pp. 158–172, 2016. doi: 10.1016/j.automatica.2016.03.021
    X. Ge, Q.-L. Han, and Z. Wang, “A dynamic event-triggered transmission scheme for distributed set-membership estimation over wireless sensor networks,” IEEE Trans. Cybernetics, vol. 49, no. 1, pp. 171–183, 2019. doi: 10.1109/TCYB.2017.2769722
    L. Zou, Z. Wang, Q.-L. Han, and D. Zhou, “Full information estimation for time-varying systems subject to Round-Robin scheduling: A recursive filter approach,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 51, no. 3, pp. 1904–1916, 2021. doi: 10.1109/TSMC.2019.2907620
    G. Calafiore, “Reliable localization using set-valued nonlinear filters,” IEEE Trans. Systems,Man,and Cybernetics - Part A: Systems and Humans, vol. 35, no. 2, pp. 189–197, 2005. doi: 10.1109/TSMCA.2005.843383
    D. Merhy, C. Stoica Maniu, T. Alamo, E. F. Camacho, S. Ben Chabane, T. Chevet, M. Makarov, and I. Hinostroza, “Guaranteed set-membership state estimation of an octorotor’s position for radar applications,” Int. J. Control, vol. 93, no. 11, pp. 2760–2770, 2020. doi: 10.1080/00207179.2020.1825796
    J. Dong and G.-H. Yang, “ $ \substack{{\cal{H}}_{\infty}} $ filtering for continuous-time T–S fuzzy systems with partly immeasurable premise variables,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 47, no. 8, pp. 1931–1940, 2017. doi: 10.1109/TSMC.2016.2572145
    Y. Liu, B.-Z. Guo, J. H. Park, and S. Lee, “Event-based reliable dissipative filtering for T–S fuzzy systems with asynchronous constraints,” IEEE Trans. Fuzzy Systems, vol. 26, no. 4, pp. 2089–2098, 2018. doi: 10.1109/TFUZZ.2017.2762633
    F. Yang and Y. Li, “Set-membership fuzzy filtering for nonlinear discrete-time systems,” IEEE Trans. Systems,Man,and Cybernetics: Cybernetics, vol. 40, no. 1, pp. 116–124, 2010. doi: 10.1109/TSMCB.2009.2020436
    S.-J. Huang, D.-Q. Zhang, L.-D. Guo, and L.-B. Wu, “Convergent estimation mechanism design for nonlinear fuzzy systems with faults,” IEEE Trans. Cybernetics, vol. 50, no. 5, pp. 2176–2185, 2020. doi: 10.1109/TCYB.2018.2884221
    Y. Wang, H. R. Karimi, H.-K. Lam, and H. Yan, “Fuzzy output tracking control and filtering for nonlinear discrete-time descriptor systems under unreliable communication links,” IEEE Trans. Cybernetics, vol. 50, no. 6, pp. 2369–2379, 2020. doi: 10.1109/TCYB.2019.2920709
    Y. Zhao, H. Gao, and J. Qiu, “Fuzzy observer based control for nonlinear coupled hyperbolic PDE-ODE systems,” IEEE Trans. Fuzzy Systems, vol. 27, no. 7, pp. 1332–1346, 2019. doi: 10.1109/TFUZZ.2018.2877635
    H. Li, J. Wang, H. Du, and H. R. Karimi, “Adaptive sliding mode control for Takagi–Sugeno fuzzy systems and its applications,” IEEE Trans. Fuzzy Systems, vol. 26, no. 2, pp. 531–542, 2018. doi: 10.1109/TFUZZ.2017.2686357
    D. P. Bertsekas, “Feature-based aggregation and deep reinforcement learning: A survey and some new implementations,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 1–31, 2019. doi: 10.1109/JAS.2018.7511249
    W. Chang, Y. Li, and S. Tong, “Adaptive fuzzy backstepping tracking control for flexible robotic manipulator,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 12, pp. 1923–1930, 2021. doi: 10.1109/JAS.2017.7510886
    W. Li, Z. Xie, Y. Cao, P. K. Wong, and J. Zhao, “Sampled-data asynchronous fuzzy output feedback control for active suspension systems in restricted frequency domain,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 1052–1066, 2021. doi: 10.1109/JAS.2020.1003306
    Y. Wang, V. Puig, and G. Cembrano, “Set-membership approach and Kalman observer based on zonotopes for discrete-time descriptor systems,” Automatica, vol. 93, pp. 435–443, 2018. doi: 10.1016/j.automatica.2018.03.082
    A. Jiménez, B. M. Al-Hadithi, F. Matía, and R. Haber-Haber, “Improvement of Takagi-Sugeno fuzzy model for the estimation of nonlinear functions,” Asian J. Control, vol. 14, no. 2, pp. 320–334, 2012. doi: 10.1002/asjc.310
    S. P. Boyd, Linear Matrix Inequalities in System and Control Theory. Philadelphia: Society for Industrial and Applied Mathematics, 1994.


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