doi: 10.3934/dcdss.2022023
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Fault detection filtering for continuous-time singular systems under a dynamic event-triggered mechanism

1. 

Key Laboratory of Smart Manufacturing in Energy Chemical Process of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China

2. 

Information Science and Engineering, Chengdu University, Chengdu 610106, China

3. 

2 College of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China

4. 

College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, China

*Corresponding author: Huaicheng Yan

Received  October 2021 Revised  December 2021 Early access February 2022

Fund Project: The second author is supported by the National Natural Science Foundation of China (62073143, 61922063), Program of Shanghai Academic Research Leader (19XD1421000), Shanghai International Science and Technology Cooperation Project (18510711100), Shanghai and HongKong-Macao-Taiwan Science and Technology Cooperation Project (19510760200), Shanghai Shuguang Project (18SG18), and Innovation Program of Shanghai Municipal Education Commission (2021-01-07-00-02-E00107)

This paper focuses on the problem of fault detection filtering (FDF) for continuous-time singular systems via a dynamic event-triggered mechanism. Firstly, in order to reduce signal transmission and save network resources, a dynamic event-triggered mechanism is adopted. Compared with the static mechanism, the proposed method is more effective on reducing network transmission pressure since a dynamic variable is introduced. Secondly, a novel criterion is derived to guarantee the admissibility of the residual system with a certain $ \mathcal{H}_\infty $ performance. According to the derived conditions, a new method is given to codesign the desired filter and the event-triggered parameters. Finally, an example is employed to illustrate the validity of the proposed approach.

Citation: Qian Zhang, Huaicheng Yan, Jun Cheng, Xisheng Zhan, Kaibo Shi. Fault detection filtering for continuous-time singular systems under a dynamic event-triggered mechanism. Discrete and Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2022023
References:
[1]

P. Anh, P. Linh, D. Thuan and S. Trenn, Stability analysis for switched discrete-time linear singular systems, Automatica, 119 (2020), 109100, 9 pp. doi: 10.1016/j.automatica.2020.109100.

[2]

Y. CuiJ. ShenZ. Feng and Y. Chen, Stability analysis for positive singular systems with time-varying delays, IEEE Trans. Automat. Control, 63 (2018), 1487-1494.  doi: 10.1109/TAC.2017.2749524.

[3]

D. DuS. Xu and V. Cocquempot, Fault detection for nonlinear discrete-time switched systems with persistent dwell time, IEEE Transactions on Fuzzy Systems, 26 (2018), 2466-2474.  doi: 10.1109/TFUZZ.2017.2753164.

[4]

G. Duan, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010. doi: 10.1007/978-1-4419-6397-0.

[5]

A. Girard, Dynamic triggering mechanisms for event-triggered control, IEEE Trans. Automat. Control, 60 (2015), 1992-1997.  doi: 10.1109/TAC.2014.2366855.

[6]

H. LiZ. ChenL. WuH. Lam and H. Du, Event-triggered fault detection of nonlinear networked systems, IEEE Transactions on Cybernetics, 47 (2017), 1041-1052.  doi: 10.1109/TCYB.2016.2536750.

[7]

Q. LiH. Xue and C. Lu, Event-based fault detection for interval type-2 fuzzy systems with measurement outliers, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), 1301-1328.  doi: 10.3934/dcdss.2020412.

[8]

X. LiD. Peng and J. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Trans. Automat. Control, 65 (2020), 4908-4913.  doi: 10.1109/TAC.2020.2964558.

[9]

X. LiJ. ShenH. Akca and R. Rakkiyappan, LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter, Appl. Math. Comput., 250 (2015), 798-804.  doi: 10.1016/j.amc.2014.10.113.

[10]

X. Li, X. Yang and J. Cao, Event-triggered impulsive control for nonlinear delay systems, Automatica, 177 (2020), 108981, 7 pp. doi: 10.1016/j.automatica.2020.108981.

[11]

X. Li, T. Zhang and J. Wu, Input-to-state stability of impulsive systems via event-triggered impulsive control, IEEE Transactions on Cybernetics, (2020). Available from: DOI: 10.1109/TSMC.2020.2964172.

[12]

X. LiuX. SuP. ShiS. Nguang and C. Shen, Fault detection filtering for nonlinear switched systems via event-triggered communication approach, Automatica, 101 (2019), 365-376.  doi: 10.1016/j.automatica.2018.12.006.

[13]

Z. NingT. WangX. Song and J. Yu, Fault detection of nonlinear stochastic systems via a dynamic event-triggered strategy, Signal Processing, 167 (2020), 107283. 

[14]

Z. NingJ. YuY. Pan and H. Li, Adaptive event-triggered fault detection for fuzzy stochastic systems with missing measurements, IEEE Transactions on Fuzzy Systems, 26 (2018), 2201-2212.  doi: 10.1109/TFUZZ.2017.2780799.

[15]

C. Park, N. Kwon, I. Park and P. Park, $\mathcal{H}_\infty$ filtering for singular Markovian jump systems with partly unknown transition rates, Automatica, 109 (2019), 108528, 6 pp. doi: 10.1016/j.automatica.2019.108528.

[16]

Y. Pan and G. Yang, Event-triggered fault detection filter design for nonlinear networked systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2018), 1851-1862. 

[17]

H. RenS. Li and C. Lu, Event-triggered adaptive fault-tolerant control for multi-agent systems with unknown disturbances, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), 1395-1414.  doi: 10.3934/dcdss.2020379.

[18]

R. Riaza, Differential-Algebraic Systems: Analytical Aspects and Circuit Applications, World Scientific, 2008. doi: 10.1142/6746.

[19]

X. SuP. ShiL. Wu and Y. Song, Fault detection filtering for nonlinear switched stochastic systems, IEEE Trans. Automat. Control, 61 (2016), 1310-1315.  doi: 10.1109/TAC.2015.2465091.

[20]

X. Sun and Q. Zhang, Admissibility analysis for interval type-2 fuzzy descriptor systems based on sliding mode control, IEEE Transactions on Cybernetics, 49 (2019), 3032-3040.  doi: 10.1109/TCYB.2018.2837890.

[21]

Y. Tian, H. Yan, H. Zhang, J. Cheng and H. Shen, Asynchronous output feedback control of hidden semi-markov jump systems with random mode-dependent delays, IEEE Transactions on Automatic Control, (2021), 1–1. doi: 10.1109/TAC.2021.3110006.

[22]

H. WangY. YingR. Lu and A. Xue, Network-based $\mathcal{H}_\infty$ control for singular systems with event-triggered sampling scheme, Information Sciences, 329 (2016), 540-551. 

[23]

Z. WuJ. ParkH. SuB. Song and J. Chu, Mixed $\mathcal{H}_\infty$ and passive filtering for singular systems with time delays, Signal Processing, 93 (2013), 1705-1711. 

[24]

X. XiaoJ. ParkL. Zhou and G. Lu, New results on stability analysis of Markovian switching singular systems, IEEE Transactions on Automatic Control, 64 (2019), 2084-2091.  doi: 10.1109/TAC.2018.2863182.

[25]

Y. XuX. JinS. Wang and Y. Tang, Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), 1495-1518.  doi: 10.3934/dcdss.2020377.

[26]

M. XueH. YanH. ZhangZ. LiS. Chen and C. Chen, Event-triggered guaranteed cost controller design for T-S fuzzy Markovian jump systems with partly unknown transition probabilities, IEEE Transactions on Fuzzy Systems, 29 (2021), 1052-1064. 

[27]

M. Xue, H. Yan, H. Zhang, X. Zhan and K. Shi, Compensation-based output feedback control for fuzzy Markov jump systems with random packet losses, IEEE Transactions on Cybernetics, (2021), 1–12. doi: 10.1109/TCYB.2021.3088872.

[28]

H. YanJ. HanH. ZhangX. Zhan and Y. Wang, Adaptive event-triggered predictive control for finite time microgrid, IEEE Trans. Circuits Syst. I. Regul. Pap., 67 (2020), 1035-1044.  doi: 10.1109/TCSI.2019.2953958.

[29]

H. YanJ. WangH. ZhangH. Shen and X. Zhan, Event-based security control for stochastic networked systems subject to attacks, IEEE Transactions on System, Man, and Cybernetics: Systems, 50 (2020), 4643-4654.  doi: 10.1109/TSMC.2018.2856819.

[30]

R. YangH. ZhangG. FengH. Yan and Z. Wang, Robust cooperative output regulation of multi-agent systems via adaptive event-triggered control, Automatica, 102 (2019), 129-136.  doi: 10.1016/j.automatica.2019.01.001.

[31]

D. ZhangQ. Han and X. Jia, Network-based output tracking control for T-S fuzzy systems using an event-triggered communication scheme, Fuzzy Sets and Systems, 273 (2015), 26-48.  doi: 10.1016/j.fss.2014.12.015.

[32]

L. ZhangS. NguangD. Ouyang and S. Yan, Synchronization of delayed neural networks via integral-based event-triggered scheme, IEEE Trans. Neural Netw. Learn. Syst., 31 (2020), 5092-5102.  doi: 10.1109/TNNLS.2019.2963146.

[33]

Q. Zhang, C. Liu and X. Zhang, Complexity, Analysis and Control of Singular Biological Systems, Springer-Verlag, London, 2012. doi: 10.1007/978-1-4471-2303-3.

[34]

Q. ZhangH. YanH. ZhangS. Chen and M. Wang, $H_\infty$ control of singular system based on stochastic cyber-attacks and dynamic event-triggered mechanism, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 5 (2021), 7510-7516. 

[35]

Y. ZhangY. MaL. FuW. Zhao and X. Huang, Finite-time non-fragile $\mathcal{H}_\infty$ sampled-data control for uncertain T-S fuzzy system with time-varying delay and nonlinear perturbation subject to Markovian jump, ISA Transactions, 99 (2020), 59-73. 

[36]

Y. ZhangQ. ZhangJ. Zhang and Y. Wang, Sliding mode control for fuzzy singular systems with time delay based on vector integral sliding mode surface, IEEE Transactions on Fuzzy Systems, 28 (2020), 768-782. 

[37]

L. ZhaoX. YangW. Zhang and L. Yu, Progressive information filtering fusion for multi-sensor nonlinear systems, Signal Processing, 163 (2019), 181-187.  doi: 10.1016/j.sigpro.2019.05.023.

[38]

G. ZhuangJ. XiaY. Chu and F. Chen, $\mathcal{H}_\infty$ mode-dependent fault detection filter design for stochastic Markovian jump systems with time-varying delays and parameter uncertainties, ISA Transactions, 53 (2014), 1024-1034. 

show all references

References:
[1]

P. Anh, P. Linh, D. Thuan and S. Trenn, Stability analysis for switched discrete-time linear singular systems, Automatica, 119 (2020), 109100, 9 pp. doi: 10.1016/j.automatica.2020.109100.

[2]

Y. CuiJ. ShenZ. Feng and Y. Chen, Stability analysis for positive singular systems with time-varying delays, IEEE Trans. Automat. Control, 63 (2018), 1487-1494.  doi: 10.1109/TAC.2017.2749524.

[3]

D. DuS. Xu and V. Cocquempot, Fault detection for nonlinear discrete-time switched systems with persistent dwell time, IEEE Transactions on Fuzzy Systems, 26 (2018), 2466-2474.  doi: 10.1109/TFUZZ.2017.2753164.

[4]

G. Duan, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010. doi: 10.1007/978-1-4419-6397-0.

[5]

A. Girard, Dynamic triggering mechanisms for event-triggered control, IEEE Trans. Automat. Control, 60 (2015), 1992-1997.  doi: 10.1109/TAC.2014.2366855.

[6]

H. LiZ. ChenL. WuH. Lam and H. Du, Event-triggered fault detection of nonlinear networked systems, IEEE Transactions on Cybernetics, 47 (2017), 1041-1052.  doi: 10.1109/TCYB.2016.2536750.

[7]

Q. LiH. Xue and C. Lu, Event-based fault detection for interval type-2 fuzzy systems with measurement outliers, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), 1301-1328.  doi: 10.3934/dcdss.2020412.

[8]

X. LiD. Peng and J. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Trans. Automat. Control, 65 (2020), 4908-4913.  doi: 10.1109/TAC.2020.2964558.

[9]

X. LiJ. ShenH. Akca and R. Rakkiyappan, LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter, Appl. Math. Comput., 250 (2015), 798-804.  doi: 10.1016/j.amc.2014.10.113.

[10]

X. Li, X. Yang and J. Cao, Event-triggered impulsive control for nonlinear delay systems, Automatica, 177 (2020), 108981, 7 pp. doi: 10.1016/j.automatica.2020.108981.

[11]

X. Li, T. Zhang and J. Wu, Input-to-state stability of impulsive systems via event-triggered impulsive control, IEEE Transactions on Cybernetics, (2020). Available from: DOI: 10.1109/TSMC.2020.2964172.

[12]

X. LiuX. SuP. ShiS. Nguang and C. Shen, Fault detection filtering for nonlinear switched systems via event-triggered communication approach, Automatica, 101 (2019), 365-376.  doi: 10.1016/j.automatica.2018.12.006.

[13]

Z. NingT. WangX. Song and J. Yu, Fault detection of nonlinear stochastic systems via a dynamic event-triggered strategy, Signal Processing, 167 (2020), 107283. 

[14]

Z. NingJ. YuY. Pan and H. Li, Adaptive event-triggered fault detection for fuzzy stochastic systems with missing measurements, IEEE Transactions on Fuzzy Systems, 26 (2018), 2201-2212.  doi: 10.1109/TFUZZ.2017.2780799.

[15]

C. Park, N. Kwon, I. Park and P. Park, $\mathcal{H}_\infty$ filtering for singular Markovian jump systems with partly unknown transition rates, Automatica, 109 (2019), 108528, 6 pp. doi: 10.1016/j.automatica.2019.108528.

[16]

Y. Pan and G. Yang, Event-triggered fault detection filter design for nonlinear networked systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2018), 1851-1862. 

[17]

H. RenS. Li and C. Lu, Event-triggered adaptive fault-tolerant control for multi-agent systems with unknown disturbances, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), 1395-1414.  doi: 10.3934/dcdss.2020379.

[18]

R. Riaza, Differential-Algebraic Systems: Analytical Aspects and Circuit Applications, World Scientific, 2008. doi: 10.1142/6746.

[19]

X. SuP. ShiL. Wu and Y. Song, Fault detection filtering for nonlinear switched stochastic systems, IEEE Trans. Automat. Control, 61 (2016), 1310-1315.  doi: 10.1109/TAC.2015.2465091.

[20]

X. Sun and Q. Zhang, Admissibility analysis for interval type-2 fuzzy descriptor systems based on sliding mode control, IEEE Transactions on Cybernetics, 49 (2019), 3032-3040.  doi: 10.1109/TCYB.2018.2837890.

[21]

Y. Tian, H. Yan, H. Zhang, J. Cheng and H. Shen, Asynchronous output feedback control of hidden semi-markov jump systems with random mode-dependent delays, IEEE Transactions on Automatic Control, (2021), 1–1. doi: 10.1109/TAC.2021.3110006.

[22]

H. WangY. YingR. Lu and A. Xue, Network-based $\mathcal{H}_\infty$ control for singular systems with event-triggered sampling scheme, Information Sciences, 329 (2016), 540-551. 

[23]

Z. WuJ. ParkH. SuB. Song and J. Chu, Mixed $\mathcal{H}_\infty$ and passive filtering for singular systems with time delays, Signal Processing, 93 (2013), 1705-1711. 

[24]

X. XiaoJ. ParkL. Zhou and G. Lu, New results on stability analysis of Markovian switching singular systems, IEEE Transactions on Automatic Control, 64 (2019), 2084-2091.  doi: 10.1109/TAC.2018.2863182.

[25]

Y. XuX. JinS. Wang and Y. Tang, Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), 1495-1518.  doi: 10.3934/dcdss.2020377.

[26]

M. XueH. YanH. ZhangZ. LiS. Chen and C. Chen, Event-triggered guaranteed cost controller design for T-S fuzzy Markovian jump systems with partly unknown transition probabilities, IEEE Transactions on Fuzzy Systems, 29 (2021), 1052-1064. 

[27]

M. Xue, H. Yan, H. Zhang, X. Zhan and K. Shi, Compensation-based output feedback control for fuzzy Markov jump systems with random packet losses, IEEE Transactions on Cybernetics, (2021), 1–12. doi: 10.1109/TCYB.2021.3088872.

[28]

H. YanJ. HanH. ZhangX. Zhan and Y. Wang, Adaptive event-triggered predictive control for finite time microgrid, IEEE Trans. Circuits Syst. I. Regul. Pap., 67 (2020), 1035-1044.  doi: 10.1109/TCSI.2019.2953958.

[29]

H. YanJ. WangH. ZhangH. Shen and X. Zhan, Event-based security control for stochastic networked systems subject to attacks, IEEE Transactions on System, Man, and Cybernetics: Systems, 50 (2020), 4643-4654.  doi: 10.1109/TSMC.2018.2856819.

[30]

R. YangH. ZhangG. FengH. Yan and Z. Wang, Robust cooperative output regulation of multi-agent systems via adaptive event-triggered control, Automatica, 102 (2019), 129-136.  doi: 10.1016/j.automatica.2019.01.001.

[31]

D. ZhangQ. Han and X. Jia, Network-based output tracking control for T-S fuzzy systems using an event-triggered communication scheme, Fuzzy Sets and Systems, 273 (2015), 26-48.  doi: 10.1016/j.fss.2014.12.015.

[32]

L. ZhangS. NguangD. Ouyang and S. Yan, Synchronization of delayed neural networks via integral-based event-triggered scheme, IEEE Trans. Neural Netw. Learn. Syst., 31 (2020), 5092-5102.  doi: 10.1109/TNNLS.2019.2963146.

[33]

Q. Zhang, C. Liu and X. Zhang, Complexity, Analysis and Control of Singular Biological Systems, Springer-Verlag, London, 2012. doi: 10.1007/978-1-4471-2303-3.

[34]

Q. ZhangH. YanH. ZhangS. Chen and M. Wang, $H_\infty$ control of singular system based on stochastic cyber-attacks and dynamic event-triggered mechanism, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 5 (2021), 7510-7516. 

[35]

Y. ZhangY. MaL. FuW. Zhao and X. Huang, Finite-time non-fragile $\mathcal{H}_\infty$ sampled-data control for uncertain T-S fuzzy system with time-varying delay and nonlinear perturbation subject to Markovian jump, ISA Transactions, 99 (2020), 59-73. 

[36]

Y. ZhangQ. ZhangJ. Zhang and Y. Wang, Sliding mode control for fuzzy singular systems with time delay based on vector integral sliding mode surface, IEEE Transactions on Fuzzy Systems, 28 (2020), 768-782. 

[37]

L. ZhaoX. YangW. Zhang and L. Yu, Progressive information filtering fusion for multi-sensor nonlinear systems, Signal Processing, 163 (2019), 181-187.  doi: 10.1016/j.sigpro.2019.05.023.

[38]

G. ZhuangJ. XiaY. Chu and F. Chen, $\mathcal{H}_\infty$ mode-dependent fault detection filter design for stochastic Markovian jump systems with time-varying delays and parameter uncertainties, ISA Transactions, 53 (2014), 1024-1034. 

Figure 1.  The structure of event-triggered FDF for singular systems
Figure 2.  The residual evaluation function $ \psi(t) $
Figure 3.  Release instants under dynamic event-triggered mechanism
Figure 4.  Release instants under static event-triggered mechanism
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