A Double Sensitive Fault Detection Filter for Positive Markovian Jump Systems With A Hybrid Event-Triggered Mechanism

Junfeng Zhang; Baozhu Du; Suhuan Zhang; Shihong Ding

doi:10.1109/JAS.2024.124677

Volume 11 Issue 11

Nov. 2024

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2024 > 11(11): 2298-2315

J. Zhang, B. Du, S. Zhang, and S. Ding, “A double sensitive fault detection filter for positive Markovian jump systems with a hybrid event-triggered mechanism,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 11, pp. 2298–2315, Nov. 2024. doi: 10.1109/JAS.2024.124677

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J. Zhang, B. Du, S. Zhang, and S. Ding, “A double sensitive fault detection filter for positive Markovian jump systems with a hybrid event-triggered mechanism,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 11, pp. 2298–2315, Nov. 2024. doi: 10.1109/JAS.2024.124677

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A Double Sensitive Fault Detection Filter for Positive Markovian Jump Systems With A Hybrid Event-Triggered Mechanism

doi: 10.1109/JAS.2024.124677

Funds: This work was supported by the National Natural Science Foundation of China (62073111, 62073167), the Natural Science Foundation of Hainan Province (621QN212), and Science Research Funding of Hainan University (KYQD(ZR)22180)

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Author Bio:
Junfeng Zhang (Senior Member IEEE) received the Ph.D. degree in control science and engineering from Shanghai Jiao Tong University in 2014. Now, he is a Professor at the School of Information and Communication Engineering, Hainan University. From December 2014 to May 2022, he worked in the School of Automation, Hangzhou Dianzi University. From August 2019 to August 2020, he visited Inria, University of Lille, France. His research interests include positive systems, switched systems, and model predictive control. He was the Co-Chair of Program Committee in the 6th International Conference on Positive Systems. He has published more than 50 journal and conference papers and one book in the field of positive systems

Baozhu Du received the B.S. degree in information and computing science, and the M.S. degree in operational research and cybernetics from Northeastern University in 2003 and 2006, respectively, the Ph.D. degree in mechanical engineering from The University of Hong Kong, China in 2010. From 2017 to 2019, she was an Alexander von Humboldt experienced Researcher in University of Duisburg-Essen, Germany. Now, she is a Professor in the School of Information and Communication Engineering, Hainan University. Her research interests include stability analysis and robust control/filter theory of time-delay systems, positive systems, Markovian jump systems, and networked control systems

Suhuan Zhang received the M.S. degree in control science and engineering from Hangzhou Dianzi University in 2022. She is currently a Ph.D. candidate in control science and engineering with the College of Electronics and Information Engineering, Tongji University. Her research interests include semi-Markovian (Markovian) jump systems, multi-agent systems, unknown input observer, and event-triggered control and filtering

Shihong Ding (Member IEEE) received the B.E. degree in mathematics from Anhui Normal University in 2004, and the M.S. and Ph.D. degrees in automatic control from Southeast University in 2007 and 2010, respectively. During the graduate studies, he visited The University of Texas at San Antonio, USA from August 2008 to August 2009. After graduation, he held a Research Fellowship with the University of Western Sydney, Australia for one year. He also visited Yeungnam University, South Korea, from July 2018 to August 2018 and RMIT University, Australia from December 2019 to February 2020, respectively. Since June 2010, he has been with the School of Electrical and Information Engineering, Jiangsu University, where he is currently a Full Professor. His research interests include sliding mode control and finite-time stability. He currently serves as a Subject Editor of Nonlinear Dynamics and an Associate Editor of International Journal of Adaptive Control and Signal Processing
Corresponding author: Baozhu Du, e-mail: [email protected]
Received Date: 2024-04-24
Accepted Date: 2024-07-17

Abstract

Abstract

This paper is concerned with the double sensitive fault detection filter for positive Markovian jump systems. A new hybrid adaptive event-triggered mechanism is proposed by introducing a non-monotonic adaptive law. A linear adaptive event-triggered threshold is established by virtue of 1-norm inequality. Under such a triggering strategy, the original system can be transformed into an interval uncertain system. By using a stochastic copositive Lyapunov function, an asynchronous fault detection filter is designed for positive Markovian jump systems (PMJSs) in terms of linear programming. The presented filter satisfies both $ L_{-} $-gain ($ \ell_{-} $-gain) fault sensitivity and $ L_{1} $ ($ \ell_{1} $) internal differential privacy sensitivity. The proposed approach is also extended to the discrete-time case. Finally, two examples are provided to illustrate the effectiveness of the proposed design.
- Fault detection filter,
- hybrid event-triggered mechanism,
- positive Markovian jump systems (PMJSs),
- sensitivity

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References(45)

References

[1]	L. Farina and S. Rinaldi, Positive Linear Systems: Theory and Applications, New York, USA: Wiley, 2000.
[2]	P. Bolzern, P. Colaneri, and G. De Nicolao, “Stochastic stability of positive Markov jump linear systems,” Automatica, vol. 50, no. 4, pp. 1181–1187, 2014. doi: 10.1016/j.automatica.2014.02.016
[3]	J. Zhang, Z. Han, and F. Zhu, “Stochastic stability and stabilization of positive systems with Markovian jump parameters,” Nonlinear Analysis Hybrid Syst., vol. 12, pp. 147–155, 2014. doi: 10.1016/j.nahs.2013.12.002
[4]	S. Zhu, Q.-L. Han, and C. Zhang, “L₁-stochastic stability and L₁-gain performance of positive Markov jump linear systems with time-delays: Necessary and sufficient conditions,” IEEE Trans. Autom. Control, vol. 62, no. 7, pp. 3634–3639, 2017. doi: 10.1109/TAC.2017.2671035
[5]	H. Trinh, “Delay-dependent stability and stabilisation of two-dimensional positive Markov jump systems with delays,” IET Control Theory Appl., vol. 11, no. 10, pp. 1603–1610, 2017. doi: 10.1049/iet-cta.2016.1358
[6]	L. V. Hien, “An LP approach to full-order and reduced-order state estimations of positive Markov jump systems with delay,” Int. J. Syst. Sci., vol. 48, no. 12, pp. 2534–2543, 2017. doi: 10.1080/00207721.2017.1324066
[7]	D. Krokavec and A. Filasová, “H_∞ norm principle in residual filter design for discrete-time linear positive systems,” Eur. J. Control, vol. 45, pp. 17–29, 2019. doi: 10.1016/j.ejcon.2018.10.001
[8]	X. Deng, J. Zhang, and T. Raïssi, “Event-triggered positive $l_1$-gain non-fragile filter design for positive Markov jump systems,” Inf. Sci., vol. 573, pp. 562–584, 2021. doi: 10.1016/j.ins.2021.02.030
[9]	M. Massoumnia, “A geometric approach to the synthesis of failure detection filters,” IEEE Trans. Autom. Control, vol. 31, no. 9, pp. 839–846, 1986. doi: 10.1109/TAC.1986.1104419
[10]	J. White and J. Speyer, “Detection filter design: Spectral theory and algorithms,” IEEE Trans. Autom. Control, vol. 32, no. 7, pp. 593–603, 1987. doi: 10.1109/TAC.1987.1104682
[11]	J. Chen and R. Kumar, “Fault detection of discrete-time stochastic systems subject to temporal logic correctness requirements,” IEEE Trans. Autom. Sci. Eng., vol. 12, no. 4, pp. 1369–1379, 2015. doi: 10.1109/TASE.2015.2453193
[12]	S. Liu, M. Gao, Y. Feng, and L. Sheng, “Dynamic event-triggered fault detection for rotary steerable systems with unknown time-varying noise covariances,” ISA Trans., vol. 142, pp. 478–491, 2023. doi: 10.1016/j.isatra.2023.08.018
[13]	L. Zhang, Y. Sun, Y. Pan, and H. K. Lam, “Reduced-order fault detection filter design for fuzzy semi-Markov jump systems with partly unknown transition rates,” IEEE Trans. Syst. Man Cybern. Syst., vol. 52, no. 12, pp. 7702–7713, 2022. doi: 10.1109/TSMC.2022.3163719
[14]	J. Wang, G. Yang, and J. Liu, “An LMI approach to H₋ index and mixed H₋/H_∞ fault detection observer design,” Automatica, vol. 43, no. 9, pp. 1656–1665, 2007. doi: 10.1016/j.automatica.2007.02.019
[15]	J. Han, X. Liu, X. Xie, and X. Wei, “Adaptive adjustable dimension observer based fault estimation for switched fuzzy systems with unmeasurable premise variables,” Fuzzy Sets Syst., vol. 452, pp. 149–167, 2023. doi: 10.1016/j.fss.2022.06.017
[16]	S. Huang, Z. Xiang, and H. R. Karimi, “Mixed L₋/L₁ fault detection filter design for fuzzy positive linear systems with time-varying delays,” IET Control Theory Appl., vol. 8, no. 12, pp. 1023–1031, 2014. doi: 10.1049/iet-cta.2013.0308
[17]	M. Raza, A. Khan, G. Mustafa, and M. Abid, “Design of fault detection and isolation filter for switched control systems under asynchronous switching,” IEEE Trans. Control Syst. Technol., vol. 24, no. 1, pp. 13–23, 2015.
[18]	J. Li and G. Yang, “Asynchronous fault detection filter design approach for discrete-time switched linear systems,” Int. J. Robust Nonlinear Control, vol. 24, no. 1, pp. 70–96, 2014. doi: 10.1002/rnc.2875
[19]	P. Tabuada, “Event-triggered real-time scheduling of stabilizing control tasks,” IEEE Trans. Autom. Control, vol. 52, no. 9, pp. 1680–1685, 2007. doi: 10.1109/TAC.2007.904277
[20]	S. Liu, B. Niu, G. Zong, X. Zhao, and N. Xu, “Adaptive neural dynamic-memory event-triggered control of high-order random nonlinear systems with deferred output constraints,” IEEE Trans. Autom. Sci. Eng., vol. 21, no. 3, pp. 2779–2791, 2024.
[21]	M. Davoodi, N. Meskin, and K. Khorasani, “Event-triggered multiobjective control and fault diagnosis: A unified framework,” IEEE Trans. Ind. Informat., vol. 13, no. 1, pp. 298–311, 2016.
[22]	X. Ge, Q.-L. Han, X. M. Zhang, and D. Ding, “Dynamic event-triggered control and estimation: A survey,” Int. J. Autom. Comput., vol. 18, no. 6, pp. 857–886, 2021. doi: 10.1007/s11633-021-1306-z
[23]	A. Molin and S. Hirche, “Adaptive event-triggered control over a shared network,” in Proc. Conf. Dec. Control, 2012, pp. 6591–6596.
[24]	A. Girard, “Dynamic triggering mechanisms for event-triggered control,” IEEE Trans. Autom. Control, vol. 60, no. 7, pp. 1992–1997, 2015. doi: 10.1109/TAC.2014.2366855
[25]	A. Sahoo, H. Xu, and S. Jagannathan, “Adaptive neural network-based event-triggered control of single-input single-output nonlinear discrete-time systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 1, pp. 151–164, 2015.
[26]	Y. Tan, M. Xiong, B. Zhang, and S. Fei, “Adaptive event-triggered nonfragile state estimation for fractional-order complex networked systems with cyber attacks,” IEEE Trans. Syst. Man Cybern. Syst., vol. 52, no. 4, pp. 2121–2133, 2021.
[27]	J. Liu, L. Wei, J. Cao, and S. Fei, “Hybrid-driven H_∞ filter design for T-S fuzzy systems with quantization,” Nonlinear Analysis Hybrid Syst., vol. 31, pp. 135–152, 2019. doi: 10.1016/j.nahs.2018.08.007
[28]	J. Cao, D. Ding, J. Liu, E. Tian, S. Hu, and X. Xie, “Hybrid-triggered-based security controller design for networked control system under multiple cyber attacks,” Inf. Sci., vol. 548, pp. 69–84, 2021. doi: 10.1016/j.ins.2020.09.046
[29]	S. Xiao, Y. Zhang, and B. Zhang, “Event-triggered networked fault detection for positive Markovian systems,” Signal Process., vol. 157, pp. 161–169, 2019. doi: 10.1016/j.sigpro.2018.11.014
[30]	J. Zhang, T. Raïssi, Y. Shao, and X. Cai, “Event-triggered filter design of positive systems with state saturation,” IEEE Syst. J., vol. 15, no. 3, pp. 4281–4292, 2021. doi: 10.1109/JSYST.2020.3019489
[31]	K. Yin and D. Yang, “Output feedback l₁ control of positive Markov jump systems: A dynamic event-triggered method,” J. Franklin Inst., vol. 359, no. 8, pp. 3631–3655, 2022. doi: 10.1016/j.jfranklin.2022.03.003
[32]	J. Le Ny and G. J. Pappas, “Differentially private filtering,” IEEE Trans. Autom. Control, vol. 59, no. 2, pp. 341–354, 2013.
[33]	J. Cortés, G. E. Dullerud, S. Han, J. Le Ny, S. Mitra, and G. J. Pappas, “Differential privacy in control and network systems,” in Proc. Conf. Deci. Control, 2016, pp. 4252–4272.
[34]	J. Le Ny, “Privacy-preserving nonlinear observer design using contraction analysis,” in Proc. Conf. Dec. Control, 2015, pp. 4499–4504.
[35]	E. Nozari, P. Tallapragada, and J. Cortés, “Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design,” Automatica, vol. 81, pp. 221–231, 2017. doi: 10.1016/j.automatica.2017.03.016
[36]	X. K. Liu, J. F. Zhang, and J. Wang, “Differentially private consensus algorithm for continuous-time heterogeneous multi-agent systems,” Automatica, vol. 122, p. 109283, 2020. doi: 10.1016/j.automatica.2020.109283
[37]	Y. Wang, Z. Huang, S. Mitra, and G. E. Dullerud, “Differential privacy in linear distributed control systems: Entropy minimizing mechanisms and performance tradeoffs,” IEEE Trans. Control Net. Syst., vol. 4, no. 1, pp. 118–130, 2017. doi: 10.1109/TCNS.2017.2658190
[38]	A. McGlinchey and O. Mason, “Differential privacy and the ℓ₁ sensitivity of positive linear observers,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 3111–3116, 2017. doi: 10.1016/j.ifacol.2017.08.317
[39]	R. Shorten, F. Wirth, and D. Leith, “A positive systems model of TCP-like congestion control: Asymptotic results,” IEEE/ACM Trans. Network., vol. 14, no. 3, pp. 616–629, 2006. doi: 10.1109/TNET.2006.876178
[40]	M. E. Valcher and P. Misra, “On the stabilizability and consensus of positive homogeneous multi-agent dynamical systems,” IEEE Trans. Autom. Control, vol. 59, no. 7, pp. 1936–1941, 2013.
[41]	J. Han, X. Liu, X. Xie, and X. Wei, “Dynamic output feedback fault tolerant control for switched fuzzy systems with fast time varying and unbounded faults,” IEEE Trans. Fuzzy Syst., vol. 31, no. 9, pp. 3185–3196, 2023. doi: 10.1109/TFUZZ.2023.3246061
[42]	W. W. Eckenfelder and D. J. O’Connor, Biological Waste Treatment, New York, USA: Elsevier, 1961.
[43]	K. V. Gernaey, M. C. Van Loosdrecht, M. Henze, M. Lind, and S. B. Jørgensen, “Activated sludge wastewater treatment plant modelling and simulation: State of the art,” Environ. Modell. Softw., vol. 19, no. 9, pp. 763–783, 2004. doi: 10.1016/j.envsoft.2003.03.005
[44]	A. Khanafer, T. Başar, and B. Gharesifard, “Stability of epidemic models over directed graphs: A positive systems approach,” Automatica, vol. 74, pp. 126–134, 2016. doi: 10.1016/j.automatica.2016.07.037
[45]	C. Ocampo-Martinez, V. Puig, G. Cembrano, and J. Quevedo, “Application of predictive control strategies to the management of complex networks in the urban water cycle [applications of control],” IEEE Control Syst., vol. 33, no. 1, pp. 15–41, 2013. doi: 10.1109/MCS.2012.2225919

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A non-monotonic adaptive triggering law is established for PMJSs
Asynchronous filters with double sensitivity are proposed for PMJSs
A simple analysis and design approach is presented by combining stochastic co-positive Lyapunov function and linear programming

A Double Sensitive Fault Detection Filter for Positive Markovian Jump Systems With A Hybrid Event-Triggered Mechanism

doi: 10.1109/JAS.2024.124677

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通讯作者: 陈斌, [email protected]

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