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

Yanzheng Zhu; Nuo Xu; Fen Wu; Xinkai Chen; Donghua Zhou

doi:10.1109/JAS.2023.123990

Volume 11 Issue 2

Feb. 2024

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2024 > 11(2): 418-429

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

Citation:

PDF( 2702 KB)

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

Author Bio:
Yanzheng Zhu (Senior Member, IEEE) received the Ph.D. degree in control science and engineering from the Harbin Institute of Technology in January 2016. From 2013 to 2015, he was a joint Ph.D. candidate with the Department of Electrical and Computer Engineering, Ohio State University, USA. From 2016 to 2018, he was a Postdoctoral Researcher with the College of Electrical Engineering and Automation, Shandong University of Science and Technology. From 2017 to 2019, he was a Research Fellow with the School of Computing, Engineering and Mathematics, Western Sydney University, Australia. From 2019 to 2022, he was a Full Professor with the College of Mechanical Engineering and Automation, Huaqiao University. He is currently a Full Professor with the College of Electrical Engineering and Automation, Shandong University of Science and Technology. His research interests include nondeterministic switched systems, fault diagnosis and tolerant control, and their applications. Prof. Zhu serves as an Associate Editor for IEEE Control Systems Letters and Journal of The Franklin Institute, and was a Guest Editor for European Journal of Control

Nuo Xu received the B.S. and M.S. degrees in computer science and technology both from Tiangong University, in 2017 and 2020, respectively. He is now pursuing the Ph.D. degree with the College of Mechanical Engineering and Automation, Huaqiao University. His research interests include Markov jump systems, piecewise affine systems, and their applications

Fen Wu (Senior Member, IEEE) received the B.S. and M.S. degrees in automatic control from Beijing University of Aeronautics and Astronautics in 1985 and 1988, respectively, and the Ph.D. degree in mechanical engineering from the University of California at Berkeley, USA, in 1995. From 1995 to 1997, he was a Research Associate with the Centre for Process Systems Engineering, Imperial College of Science, Technology and Medicine, UK. He was a Staff Engineer with Dynacs Engineering Company Inc., USA, from 1997 to 1999. He is currently a Professor with the Department of Mechanical and Aerospace Engineering, North Carolina State University, USA. He has authored over 170 conference papers and journal articles. His current research interests include linear parameter-varying and switching control of nonlinear systems, robust control subject to physical constraints, nonlinear control using sum-of-square programming, distributed control of multiagent systems, and the application of advanced control and optimization techniques to aerospace, mechanical, and chemical engineering problems. He is currently serving as AE for IEEE Transactions on Cybernetics and International Journal of Mechanical Systems Dynamics. Dr. Wu is a Fellow of ASME. He was an Associate Editor of the Journal of Dynamic Systems, Measurement and Control (ASME), the IEEE Transactions on Automatic Control, and the Automatica

Xinkai Chen (Fellow, IEEE) received the Ph.D. degree in engineering from Nagoya University, Japan, in 1999. He is currently a Professor with the Department of Electronic and Information Systems, Shibaura Institute of Technology, Japan. His research interests include adaptive control, smart materials, hysteresis, sliding mode control, machine vision, and observer. Dr. Chen has served as an Associate Editor for several journals, including IEEE Transactions on Automatic Control, IEEE Transactions on Control Systems Technology, IEEE Transactions on Industrial Electronics, IEEE/ASME Transactions on Mechatronics, European Journal of Control, etc. He has also served for international conferences as organizing committee members including General Chairs, Program Chairs, General Co-Chairs, Program Co-Chairs, etc

Donghua Zhou (Fellow, IEEE) received the B.Eng., M.Sc., and doctoral degrees in electrical engineering from Shanghai Jiao Tong University, in 1985, 1988, and 1990, respectively. He was an Alexander von Humboldt Research Fellow with the University of Duisburg, Germany, from 1995 to 1996, and a Visiting Scholar with Yale University, USA, from 2001 to 2002. He joined Tsinghua University in 1996, and was promoted as a Full Professor in 1997, and was the Head of the Department of Automation from 2008 to 2015. He is currently a Vice-President of Shandong University of Science and Technology and a Joint Professor with Tsinghua university. He has authored and coauthored over 230 peer-reviewed international journal papers and nine monographs in the areas of fault diagnosis, fault-tolerant control, and operational safety evaluation. Dr. Zhou was the NOC Chair of the 6th IFAC Symposium on SAFEPROCESS 2006. He is an Associate Editor of the Journal of Process Control the Vice-Chairman of the Chinese Association of Automation (CAA), a Member of IFAC TC on SAFEPROCESS, and a Fellow of IET and CAA
Corresponding author: Donghua Zhou, e-mail: zdh@mail.tsinghua.edu.cn
Received Date: 2023-08-11
Accepted Date: 2023-09-24

Available Online: 2023-11-24

Abstract

Abstract

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.
- Current feedback,
- fault estimation,
- iterative learning observer,
- Markov jump piecewise-affine system

FullText(HTML)

References(34)

References

[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
[2]	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
[3]	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
[4]	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
[5]	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
[6]	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
[7]	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
[8]	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
[9]	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
[10]	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
[11]	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
[12]	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
[13]	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
[14]	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
[15]	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
[16]	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
[17]	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
[18]	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
[19]	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
[20]	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
[21]	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
[22]	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
[23]	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
[24]	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
[25]	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
[26]	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
[27]	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
[28]	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
[29]	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
[30]	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
[31]	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
[32]	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
[33]	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
[34]	M. Kvasnica, P. Grieder, M. Baotić, and F. J. Christophersen, Multi-Parametric Toolbox (MPT). 2006.

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(7)

Get Citation

PDF

XML

Article Metrics

Article views (378) PDF downloads(68)

Highlights

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

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

doi: 10.1109/JAS.2023.123990

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Highlights

Export File

Citation

Format

Content