Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

Jingyang Mao; Xiangyu Meng; Derui Ding

doi:10.1109/JAS.2022.105416

Volume 9 Issue 6

Jun. 2022

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

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(6): 1026-1036

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

Citation:

PDF( 1473 KB)

Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

doi: 10.1109/JAS.2022.105416

Jingyang Mao^1
,,
Xiangyu Meng^{3
,
,},
Derui Ding^{1, 2
,}

1.
Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
2.
School of Science, Computing and Engineering Technologies, Swinburne University of Technology, Melbourne, VIC 3122, Australia
3.
Division of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, LA, 70803 USA

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

Author Bio:
Jingyang Mao received the B.Sc. degree in mathematics and applied mathematics from University of Shanghai for Science and Technology, Shanghai, China, in 2015, where he is currently pursuing the Ph.D. degree in control science and engineering.From September 2019 to September 2021, he was a visiting scholar in the Department of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, LA, USA. His research interests include networked control systems as well as protocol-based recursive filtering for nonlinear systems.Dr. Mao is also a very active reviewer for many international journals

Xiangyu Meng received the B.S. degree in information and computing science from Harbin Engineering University, and M.S. degree in control science and engineering from Harbin Institute of Technology, Harbin, China, in 2006 and 2008, respectively. He received the Ph.D. degree in electrical and computer engineering from the University of Alberta, Edmonton, Alberta, Canada, in 2014.From June 2007 to July 2007, and from November 2007 to January 2008, he was a Research Associate with the Department of Mechanical Engineering, University of Hong Kong. From February 2009 to August 2010, he was a Research Award Recipient in the Department of Electrical and Computer Engineering, University of Alberta. From December 2014 to December 2016, he was a Research Fellow with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. From January 2017 to December 2018, he was a Postdoctoral Associate with the Division of Systems Engineering, Boston University, USA. Since 2019, he has been an Assistant Professor with the Division of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, LA, USA. His research interests include connected and autonomous vehicles, multi-agent networks, and cyber-physical systems

Derui Ding (Senior Member) received both the B.Sc. degree in Industry Engineering in 2004 and the M.Sc. degree in Detection Technology and Automation Equipment in 2007 from Anhui Polytechnic University, Wuhu, China, and the Ph.D. degree in Control Theory and Control Engineering in 2014 from Donghua University, Shanghai, China.Dr. Ding is currently a Senior Research Fellow with the School of Science, Computing and Engineering Technologies, Swinburne University of Technology, Melbourne, VIC, Australia. From July 2007 to December 2014, he was a teaching assistant and then a lecturer in the Department of Mathematics, Anhui Polytechnic University, Wuhu, China. From June 2012 to September 2012, he was a research assistant in the Department of Mechanical Engineering, the University of Hong Kong, China. From March 2013 to March 2014, he was a visiting scholar in the Department of Information Systems and Computing, Brunel University London, UK. From June 2015 to August 2015, he was a research assistant in the Department of Mathematics, City University of Hong Kong, China. His research interests include nonlinear stochastic control and filtering, as well as multi-agent systems and sensor networks. He has published over 100 papers in refereed international journals.Dr. Ding is a Standing Director of the IEEE PES Intelligent Grid & Emerging Technologies Satellite Committee-China. He received the 2020 Andrew P. Sage Best Transactions Paper Award from the IEEE Systems, Man, and Cybernetics (SMC) Society, and the IET Premium Awards 2018. He is serving as an Associate Editor for Neurocomputing and IET Control Theory & Applications. He also served as a Guest Editor for several issues, including the International Journal of Systems Science, International Journal of General Systems, and Kybernetika
Corresponding author: Xiangyu Meng, e-mail: xmeng5@lsu.edu
Received Date: 2021-10-31
Accepted Date: 2021-12-15

Available Online: 2022-01-08

Abstract

Abstract

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.
- Affine model,
- membership functions,
- set-membership filtering,
- stability,
- Takagi-Sugeno fuzzy modeling

FullText(HTML)

References(29)

References

[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
[2]	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
[3]	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
[4]	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.
[5]	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
[6]	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
[7]	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
[8]	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
[9]	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
[10]	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
[11]	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
[12]	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
[13]	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
[14]	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
[15]	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
[16]	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
[17]	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
[18]	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
[19]	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
[20]	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
[21]	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
[22]	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
[23]	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
[24]	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
[25]	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
[26]	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
[27]	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
[28]	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
[29]	S. P. Boyd, Linear Matrix Inequalities in System and Control Theory. Philadelphia: Society for Industrial and Applied Mathematics, 1994.

Supplements(0)

Cited By

Proportional views

Proportional views

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

Figures(12)

Get Citation

PDF

XML

Article Metrics

Article views (547) PDF downloads(86)

Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

doi: 10.1109/JAS.2022.105416

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content