April  2021, 14(4): 1301-1328. doi: 10.3934/dcdss.2020412

Event-based fault detection for interval type-2 fuzzy systems with measurement outliers

1. 

College of Engineering, Bohai University, Jinzhou 121013, Liaoning, China

2. 

School of Mathematics and Physics, Bohai University, Jinzhou 121013, Liaoning, China

* Corresponding author: Hong Xue

Received  January 2020 Revised  April 2020 Published  April 2021 Early access  July 2020

This paper investigates the event-based fault detection (FD) problem for a category of discrete-time interval type-2 fuzzy systems with measurement outliers. For the sake of decreasing the utilization of limited communication bandwidth, an event-based mechanism is introduced. Based on the saturation function technique, a novel event-based FD observer is first designed to reduce the influence of outliers in the dynamic systems. Then, on the basis of Lyapunov stability theory, sufficient conditions are provided to ensure that the error system satisfies the $ \mathcal{H}_{\infty} $ performance and the $ \mathcal{H}_{\infty} $ fault performance in different cases, respectively. In contrast to the existing event-based FD results, the false alarm, which is induced by measurement outliers, can be effectively avoided by the designed FD observer with saturation function. Lastly, some simulation results are given to verify the effectiveness of the method presented in this paper.

Citation: Qi Li, Hong Xue, Changxin Lu. Event-based fault detection for interval type-2 fuzzy systems with measurement outliers. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1301-1328. doi: 10.3934/dcdss.2020412
References:
[1]

A. Alessandri and L. Zaccarian, Stubborn state observers for linear time-invariant systems, Automatica, 88 (2018), 1-9.  doi: 10.1016/j.automatica.2017.10.022.

[2]

A. Alessandri and M. Awawdeh, Moving-horizon estimation with guaranteed robustness for discrete-time linear systems and measurements subject to outliers, Automatica, 67 (2016), 85-93.  doi: 10.1016/j.automatica.2016.01.015.

[3]

Z. Chen, Q.-L. Han, Y. Yan and Z.-G. Wu, How often should one update control and estimation: Review of networked triggering techniques, Science China Information Sciences, 63 (2020), Paper No. 150201. doi: 10.1007/s11432-019-2637-9.

[4]

S. CourtK. Kunisch and L. Pfeiffer, Hybrid optimal control problems for a class of semilinear parabolic equations, Discrete & Continuous Dynamical Systems-S, 11 (2018), 1031-1060.  doi: 10.3934/dcdss.2018060.

[5]

H. GaoY. ZhaoJ. Lam and K. Chen, $\mathcal{H}_ {\infty}$ fuzzy filtering of nonlinear systems with intermittent measurements, IEEE Transactions on Fuzzy Systems, 17 (2008), 291-300. 

[6]

Y. GaoF. XiaoJ. Liu and and R. Wang, Distributed soft fault detection for interval type-2 fuzzy-model-based stochastic systems with wireless sensor networks, IEEE Transactions on Industrial Informatics, 15 (2018), 334-347.  doi: 10.1109/TII.2018.2812771.

[7]

H. Gao and C. Wang, Comments and further results on "A descriptor system approach to $\mathcal{H}_{\infty}$ control of linear time-delay systems", IEEE Transactions on Automatic Control, 48 (2003), 520-525.  doi: 10.1109/TAC.2003.809154.

[8]

M. A. Gandhi and L. Mili, Robust kalman filter based on a generalized maximum-likelihood-type estimator, IEEE Transactions on Signal Processing, 58 (2010), 2509-2520.  doi: 10.1109/TSP.2009.2039731.

[9]

E. Grigorieva and E. Khailov, Determination of the optimal controls for an ebola epidemic model, Discrete & Continuous Dynamical Systems-S, 11 (2018), 1071-1101.  doi: 10.3934/dcdss.2018062.

[10]

N. Hayek, Infinite-horizon multiobjective optimal control problems for bounded processes, Discrete & Continuous Dynamical Systems-S, 11 (2018), 1121-1141.  doi: 10.3934/dcdss.2018064.

[11]

H. HassaniJ. ZareiM. Chadli and J. Qiu, Unknown input observer design for interval type-2 T–S fuzzy systems with immeasurable premise variables, IEEE Transactions on Cybernetics, 47 (2017), 2639-2650.  doi: 10.1109/TCYB.2016.2602300.

[12]

H. K. Lam and L. D. Seneviratne, Stability analysis of interval type-2 fuzzy-model-based control systems, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38 (2008), 617-628.  doi: 10.1109/TSMCB.2008.915530.

[13]

X. LiX. Zhang and S. Song, Effect of delayed impulses on input-to-state stability of nonlinear systems, Automatica, 76 (2017), 378-382.  doi: 10.1016/j.automatica.2016.08.009.

[14]

Z. LiL. GaoW. Chen and Y. Xu, Distributed adaptive cooperative tracking of uncertain nonlinear fractional-order multi-agent systems, IEEE/CAA Journal of Automatica Sinica, 7 (2020), 292-300.  doi: 10.1109/JAS.2019.1911858.

[15]

H. LiJ. YuC. Hilton and H. Liu, Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T–S fuzzy approach, IEEE Transactions on Industrial Electronics, 60 (2013), 3328-3338.  doi: 10.1109/TIE.2012.2202354.

[16]

X. LiX. Yang and T. Huang, Persistence of delayed cooperative models: Impulsive control method, Applied Mathematics and Computation, 342 (2019), 130-146.  doi: 10.1016/j.amc.2018.09.003.

[17]

X. LiJ. Shen and R. Rakkiyappan, Persistent impulsive effects on stability of functional differential equations with finite or infinite delay, Applied Mathematics and Computation, 329 (2018), 14-22.  doi: 10.1016/j.amc.2018.01.036.

[18]

H. Liang, X. Guo, Y. Pan and T. Huang, Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers, IEEE Transactions on Fuzzy Systems, 2020, 1–1. doi: 10.1109/TFUZZ.2020.2982618.

[19]

H. Liang, L. Zhang, Y. Sun and T. Huang, Containment control of semi-markovian multiagent systems with switching topologies, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 1–11. doi: 10.1109/TSMC.2019.2946248.

[20]

R. LuW. YuJ. Lü and A. Xue, Synchronization on complex networks of networks, IEEE Transactions on Neural Networks and Learning Systems, 25 (2014), 2110-2118.  doi: 10.1109/TNNLS.2014.2305443.

[21]

J. M. MendelR. I. John and F. Liu, Interval type-2 fuzzy logic systems made simple, IEEE Transactions on Fuzzy Systems, 14 (2006), 808-821.  doi: 10.1109/TFUZZ.2006.879986.

[22]

J. NaY. HuangX. WuS.-F. Su and G. Li, Adaptive finite-time fuzzy control of nonlinear active suspension systems with input delay, IEEE Transactions on Cybernetics, 50 (2020), 2639-2650.  doi: 10.1109/TCYB.2019.2894724.

[23]

J. NaB. JingY. HuangG. Gao and C. Zhang, Unknown system dynamics estimator for motion control of nonlinear robotic systems, IEEE Transactions on Industrial Electronics, 67 (2020), 3850-3859.  doi: 10.1109/TIE.2019.2920604.

[24]

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.

[25]

Y. Pan, P. Du, H. Xue and H. K. Lam, Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance, IEEE Transactions on Fuzzy Systems, 2020, 1–1. doi: 10.1109/TFUZZ.2020.2999746.

[26]

Y. Pan and G. H. Yang, Event-triggered fault detection filter design for nonlinear networked systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2017), 1851-1862. 

[27]

Y. Pan and G. H. Yong, Event-driven fault detection for discrete-time interval type-2 fuzzy systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 1–2. doi: 10.1109/TSMC.2019.2945063.

[28]

C. PengQ. L. Han and D. Yue, To transmit or not to transmit: A discrete event-triggered communication scheme for networked Takagi–Sugeno fuzzy systems, IEEE Transactions on Fuzzy Systems, 21 (2013), 164-170.  doi: 10.1109/TFUZZ.2012.2199994.

[29]

P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52 (2007), 1680-1685.  doi: 10.1109/TAC.2007.904277.

[30]

M. Tong, W. Lin, X. Huo, Z. Jin and C. Miao, A model-free fuzzy adaptive trajectory tracking control algorithm based on dynamic surface control, International Journal of Advanced Robotic Systems, 17 (2020), 1729881419894417.

[31]

C. S. TsengB. S. Chen and H. J. Uang, Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model, IEEE Transactions on Fuzzy Systems, 9 (2001), 381-392. 

[32]

W. Wang, H. Liang, Y. Pan and T. Li, Prescribed performance adaptive fuzzy containment control for nonlinear multi-agent systems using disturbance observer, IEEE Transactions on Cybernetics, 2020, 1–13. doi: 10.1109/TCYB.2020.2969499.

[33]

X. L. Wang and G. H. Yang, Observer-based fault detection for T-S fuzzy systems subject to measurement outliers, Neurocomputing, 335 (2019), 21-36.  doi: 10.1016/j.neucom.2019.01.047.

[34]

Z. Wang and D. Liu, Data-based controllability and observability analysis of linear discrete-time systems, IEEE Transactions on Neural Networks, 22 (2011), 2388-2392. 

[35]

Z. WangY. XuR. Lu and H. Peng, Finite-time state estimation for coupled Markovian neural networks with sensor nonlinearities, IEEE Transactions on Neural Networks and Learning Systems, 28 (2017), 630-638.  doi: 10.1109/TNNLS.2015.2490168.

[36]

C. WuL. WuJ. Liu and Z.-P. Jiang, Active defense-based resilient sliding mode control under denial-of-service attacks, IEEE Transactions on Information Forensics and Security, 15 (2019), 237-249.  doi: 10.1109/TIFS.2019.2917373.

[37]

D. Yao, H. Li, R. Lu and Y. Shi, Distributed sliding mode tracking control of second-order nonlinear multi-agent systems: An event-triggered approach, IEEE Transactions on Cybernetics, 2020, 1–11. doi: 10.1109/TCYB.2019.2963087.

[38]

D. YangX. Li and J. Qiu, Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback, Nonlinear Analysis: Hybrid Systems, 32 (2019), 294-305.  doi: 10.1016/j.nahs.2019.01.006.

[39]

T. ZhangC. P. ChenL. ChenX. Xu and B. Hu, Design of highly nonlinear substitution boxes based on I-Ching operators, IEEE Transactions on Cybernetics, 48 (2018), 3349-3358.  doi: 10.1109/TCYB.2018.2846186.

[40]

L. Zhang, H.-K. Lam, Y. Sun and H. Liang, Fault detection for fuzzy semi-markov jump systems based on interval type-2 fuzzy approach, IEEE Transactions on Fuzzy Systems, 2019, 1–1. doi: 10.1016/j.fss.2018.05.003.

[41]

Z. ZhangH. LiangC. Wu and C. K. Ahn, Adaptive event-triggered output feedback fuzzy control for nonlinear networked systems with packet dropouts and actuator failure, IEEE Transactions on Fuzzy Systems, 27 (2019), 1793-1806.  doi: 10.1109/TFUZZ.2019.2891236.

[42]

C. ZhangJ. HuJ. Qiu and Q. Chen, Event-triggered nonsynchronized $\mathcal{H}_{\infty}$ filtering for discrete-time T–S fuzzy systems based on piecewise lyapunov functions, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47 (2017), 2330-2341. 

[43]

T. Zhang, X. Wang, X. Xu and C. P. Chen, GCB-net: Graph convolutional broad network and its application in emotion recognition, IEEE Transactions on Affective Computing, 2019, 1–1. doi: 10.1109/TAFFC.2019.2937768.

[44]

X. ZhaoH. MoK. Yan and L. Li, Type-2 fuzzy control for driving state and behavioral decisions of unmanned vehicle, IEEE/CAA Journal of Automatica Sinica, 7 (2020), 178-186.  doi: 10.1109/JAS.2019.1911810.

[45]

Q. Zhou, W. Wang, H. Ma and H. Li, Event-triggered fuzzy adaptive containment control for nonlinear multi-agent systems with unknown bouc-wen hysteresis input, IEEE Transactions on Fuzzy Systems, 2019, 1–1. doi: 10.1109/TFUZZ.2019.2961642.

[46]

S. Zhu, Y. Liu, Y. Lou and J. Cao, Stabilization of logical control networks: An event-triggered control approach, Science China Information Sciences, 63 (2020), 112203, 11 pp. doi: 10.1007/s11432-019-9898-3.

[47]

Z. Zhu, Y. Pan, Q. Zhou and C. Lu, Event-triggered adaptive fuzzy control for stochastic nonlinear systems with unmeasured states and unknown backlash-like hysteresis, IEEE Transactions on Fuzzy Systems, 2020, 1–1. doi: 10.1109/TFUZZ.2020.2973950.

[48]

Q. Zhou, W. Wang, H. Liang, M. Basin and B. Wang, Observer-based event-triggered fuzzy adaptive bipartite containment control of multi-agent systems with input quantization, IEEE Transactions on Fuzzy Systems, 2019, 1–1. doi: 10.1109/TFUZZ.2019.2953573.

show all references

References:
[1]

A. Alessandri and L. Zaccarian, Stubborn state observers for linear time-invariant systems, Automatica, 88 (2018), 1-9.  doi: 10.1016/j.automatica.2017.10.022.

[2]

A. Alessandri and M. Awawdeh, Moving-horizon estimation with guaranteed robustness for discrete-time linear systems and measurements subject to outliers, Automatica, 67 (2016), 85-93.  doi: 10.1016/j.automatica.2016.01.015.

[3]

Z. Chen, Q.-L. Han, Y. Yan and Z.-G. Wu, How often should one update control and estimation: Review of networked triggering techniques, Science China Information Sciences, 63 (2020), Paper No. 150201. doi: 10.1007/s11432-019-2637-9.

[4]

S. CourtK. Kunisch and L. Pfeiffer, Hybrid optimal control problems for a class of semilinear parabolic equations, Discrete & Continuous Dynamical Systems-S, 11 (2018), 1031-1060.  doi: 10.3934/dcdss.2018060.

[5]

H. GaoY. ZhaoJ. Lam and K. Chen, $\mathcal{H}_ {\infty}$ fuzzy filtering of nonlinear systems with intermittent measurements, IEEE Transactions on Fuzzy Systems, 17 (2008), 291-300. 

[6]

Y. GaoF. XiaoJ. Liu and and R. Wang, Distributed soft fault detection for interval type-2 fuzzy-model-based stochastic systems with wireless sensor networks, IEEE Transactions on Industrial Informatics, 15 (2018), 334-347.  doi: 10.1109/TII.2018.2812771.

[7]

H. Gao and C. Wang, Comments and further results on "A descriptor system approach to $\mathcal{H}_{\infty}$ control of linear time-delay systems", IEEE Transactions on Automatic Control, 48 (2003), 520-525.  doi: 10.1109/TAC.2003.809154.

[8]

M. A. Gandhi and L. Mili, Robust kalman filter based on a generalized maximum-likelihood-type estimator, IEEE Transactions on Signal Processing, 58 (2010), 2509-2520.  doi: 10.1109/TSP.2009.2039731.

[9]

E. Grigorieva and E. Khailov, Determination of the optimal controls for an ebola epidemic model, Discrete & Continuous Dynamical Systems-S, 11 (2018), 1071-1101.  doi: 10.3934/dcdss.2018062.

[10]

N. Hayek, Infinite-horizon multiobjective optimal control problems for bounded processes, Discrete & Continuous Dynamical Systems-S, 11 (2018), 1121-1141.  doi: 10.3934/dcdss.2018064.

[11]

H. HassaniJ. ZareiM. Chadli and J. Qiu, Unknown input observer design for interval type-2 T–S fuzzy systems with immeasurable premise variables, IEEE Transactions on Cybernetics, 47 (2017), 2639-2650.  doi: 10.1109/TCYB.2016.2602300.

[12]

H. K. Lam and L. D. Seneviratne, Stability analysis of interval type-2 fuzzy-model-based control systems, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38 (2008), 617-628.  doi: 10.1109/TSMCB.2008.915530.

[13]

X. LiX. Zhang and S. Song, Effect of delayed impulses on input-to-state stability of nonlinear systems, Automatica, 76 (2017), 378-382.  doi: 10.1016/j.automatica.2016.08.009.

[14]

Z. LiL. GaoW. Chen and Y. Xu, Distributed adaptive cooperative tracking of uncertain nonlinear fractional-order multi-agent systems, IEEE/CAA Journal of Automatica Sinica, 7 (2020), 292-300.  doi: 10.1109/JAS.2019.1911858.

[15]

H. LiJ. YuC. Hilton and H. Liu, Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T–S fuzzy approach, IEEE Transactions on Industrial Electronics, 60 (2013), 3328-3338.  doi: 10.1109/TIE.2012.2202354.

[16]

X. LiX. Yang and T. Huang, Persistence of delayed cooperative models: Impulsive control method, Applied Mathematics and Computation, 342 (2019), 130-146.  doi: 10.1016/j.amc.2018.09.003.

[17]

X. LiJ. Shen and R. Rakkiyappan, Persistent impulsive effects on stability of functional differential equations with finite or infinite delay, Applied Mathematics and Computation, 329 (2018), 14-22.  doi: 10.1016/j.amc.2018.01.036.

[18]

H. Liang, X. Guo, Y. Pan and T. Huang, Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers, IEEE Transactions on Fuzzy Systems, 2020, 1–1. doi: 10.1109/TFUZZ.2020.2982618.

[19]

H. Liang, L. Zhang, Y. Sun and T. Huang, Containment control of semi-markovian multiagent systems with switching topologies, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 1–11. doi: 10.1109/TSMC.2019.2946248.

[20]

R. LuW. YuJ. Lü and A. Xue, Synchronization on complex networks of networks, IEEE Transactions on Neural Networks and Learning Systems, 25 (2014), 2110-2118.  doi: 10.1109/TNNLS.2014.2305443.

[21]

J. M. MendelR. I. John and F. Liu, Interval type-2 fuzzy logic systems made simple, IEEE Transactions on Fuzzy Systems, 14 (2006), 808-821.  doi: 10.1109/TFUZZ.2006.879986.

[22]

J. NaY. HuangX. WuS.-F. Su and G. Li, Adaptive finite-time fuzzy control of nonlinear active suspension systems with input delay, IEEE Transactions on Cybernetics, 50 (2020), 2639-2650.  doi: 10.1109/TCYB.2019.2894724.

[23]

J. NaB. JingY. HuangG. Gao and C. Zhang, Unknown system dynamics estimator for motion control of nonlinear robotic systems, IEEE Transactions on Industrial Electronics, 67 (2020), 3850-3859.  doi: 10.1109/TIE.2019.2920604.

[24]

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.

[25]

Y. Pan, P. Du, H. Xue and H. K. Lam, Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance, IEEE Transactions on Fuzzy Systems, 2020, 1–1. doi: 10.1109/TFUZZ.2020.2999746.

[26]

Y. Pan and G. H. Yang, Event-triggered fault detection filter design for nonlinear networked systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2017), 1851-1862. 

[27]

Y. Pan and G. H. Yong, Event-driven fault detection for discrete-time interval type-2 fuzzy systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 1–2. doi: 10.1109/TSMC.2019.2945063.

[28]

C. PengQ. L. Han and D. Yue, To transmit or not to transmit: A discrete event-triggered communication scheme for networked Takagi–Sugeno fuzzy systems, IEEE Transactions on Fuzzy Systems, 21 (2013), 164-170.  doi: 10.1109/TFUZZ.2012.2199994.

[29]

P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52 (2007), 1680-1685.  doi: 10.1109/TAC.2007.904277.

[30]

M. Tong, W. Lin, X. Huo, Z. Jin and C. Miao, A model-free fuzzy adaptive trajectory tracking control algorithm based on dynamic surface control, International Journal of Advanced Robotic Systems, 17 (2020), 1729881419894417.

[31]

C. S. TsengB. S. Chen and H. J. Uang, Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model, IEEE Transactions on Fuzzy Systems, 9 (2001), 381-392. 

[32]

W. Wang, H. Liang, Y. Pan and T. Li, Prescribed performance adaptive fuzzy containment control for nonlinear multi-agent systems using disturbance observer, IEEE Transactions on Cybernetics, 2020, 1–13. doi: 10.1109/TCYB.2020.2969499.

[33]

X. L. Wang and G. H. Yang, Observer-based fault detection for T-S fuzzy systems subject to measurement outliers, Neurocomputing, 335 (2019), 21-36.  doi: 10.1016/j.neucom.2019.01.047.

[34]

Z. Wang and D. Liu, Data-based controllability and observability analysis of linear discrete-time systems, IEEE Transactions on Neural Networks, 22 (2011), 2388-2392. 

[35]

Z. WangY. XuR. Lu and H. Peng, Finite-time state estimation for coupled Markovian neural networks with sensor nonlinearities, IEEE Transactions on Neural Networks and Learning Systems, 28 (2017), 630-638.  doi: 10.1109/TNNLS.2015.2490168.

[36]

C. WuL. WuJ. Liu and Z.-P. Jiang, Active defense-based resilient sliding mode control under denial-of-service attacks, IEEE Transactions on Information Forensics and Security, 15 (2019), 237-249.  doi: 10.1109/TIFS.2019.2917373.

[37]

D. Yao, H. Li, R. Lu and Y. Shi, Distributed sliding mode tracking control of second-order nonlinear multi-agent systems: An event-triggered approach, IEEE Transactions on Cybernetics, 2020, 1–11. doi: 10.1109/TCYB.2019.2963087.

[38]

D. YangX. Li and J. Qiu, Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback, Nonlinear Analysis: Hybrid Systems, 32 (2019), 294-305.  doi: 10.1016/j.nahs.2019.01.006.

[39]

T. ZhangC. P. ChenL. ChenX. Xu and B. Hu, Design of highly nonlinear substitution boxes based on I-Ching operators, IEEE Transactions on Cybernetics, 48 (2018), 3349-3358.  doi: 10.1109/TCYB.2018.2846186.

[40]

L. Zhang, H.-K. Lam, Y. Sun and H. Liang, Fault detection for fuzzy semi-markov jump systems based on interval type-2 fuzzy approach, IEEE Transactions on Fuzzy Systems, 2019, 1–1. doi: 10.1016/j.fss.2018.05.003.

[41]

Z. ZhangH. LiangC. Wu and C. K. Ahn, Adaptive event-triggered output feedback fuzzy control for nonlinear networked systems with packet dropouts and actuator failure, IEEE Transactions on Fuzzy Systems, 27 (2019), 1793-1806.  doi: 10.1109/TFUZZ.2019.2891236.

[42]

C. ZhangJ. HuJ. Qiu and Q. Chen, Event-triggered nonsynchronized $\mathcal{H}_{\infty}$ filtering for discrete-time T–S fuzzy systems based on piecewise lyapunov functions, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47 (2017), 2330-2341. 

[43]

T. Zhang, X. Wang, X. Xu and C. P. Chen, GCB-net: Graph convolutional broad network and its application in emotion recognition, IEEE Transactions on Affective Computing, 2019, 1–1. doi: 10.1109/TAFFC.2019.2937768.

[44]

X. ZhaoH. MoK. Yan and L. Li, Type-2 fuzzy control for driving state and behavioral decisions of unmanned vehicle, IEEE/CAA Journal of Automatica Sinica, 7 (2020), 178-186.  doi: 10.1109/JAS.2019.1911810.

[45]

Q. Zhou, W. Wang, H. Ma and H. Li, Event-triggered fuzzy adaptive containment control for nonlinear multi-agent systems with unknown bouc-wen hysteresis input, IEEE Transactions on Fuzzy Systems, 2019, 1–1. doi: 10.1109/TFUZZ.2019.2961642.

[46]

S. Zhu, Y. Liu, Y. Lou and J. Cao, Stabilization of logical control networks: An event-triggered control approach, Science China Information Sciences, 63 (2020), 112203, 11 pp. doi: 10.1007/s11432-019-9898-3.

[47]

Z. Zhu, Y. Pan, Q. Zhou and C. Lu, Event-triggered adaptive fuzzy control for stochastic nonlinear systems with unmeasured states and unknown backlash-like hysteresis, IEEE Transactions on Fuzzy Systems, 2020, 1–1. doi: 10.1109/TFUZZ.2020.2973950.

[48]

Q. Zhou, W. Wang, H. Liang, M. Basin and B. Wang, Observer-based event-triggered fuzzy adaptive bipartite containment control of multi-agent systems with input quantization, IEEE Transactions on Fuzzy Systems, 2019, 1–1. doi: 10.1109/TFUZZ.2019.2953573.

Figure 1.  Estimation errors of the system
Figure 2.  Trajectory of $ \bar{\sigma}(k) $
Figure 3.  Event-based release instants and release interval
Figure 4.  Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $
Figure 5.  Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $
Figure 6.  Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $
Figure 7.  Tunnel diode circuit
Figure 8.  Estimation errors of the system
Figure 9.  Trajectory of $ \bar{\sigma}(k) $
Figure 10.  Event-based release instants and release interval
Figure 11.  Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $
Figure 12.  Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $
Figure 13.  Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $
Table 1.  Lower and upper membership functions of the system
$ {\underline{u}}_{\mathcal{L}11}(x_{1})=1-e^{-\frac{x_{1}^{2}}{1.5}} $ $ { \bar{u}}_{\mathcal{L}11}(x_{1})=1-e^{-\frac{x_{1}^{2}}{1.2}} $
$ {\underline{u}}_{\mathcal{L}21}(x_{1})=1-{\bar{u}}_{\mathcal{L}11}(x_{1}) $ $ {\bar{u}}_{\mathcal{L}21}(x_{1})=1-{\underline{u}}_{\mathcal{L}11}(x_{1}) $
$ {\underline{u}}_{\mathcal{L}11}(x_{1})=1-e^{-\frac{x_{1}^{2}}{1.5}} $ $ { \bar{u}}_{\mathcal{L}11}(x_{1})=1-e^{-\frac{x_{1}^{2}}{1.2}} $
$ {\underline{u}}_{\mathcal{L}21}(x_{1})=1-{\bar{u}}_{\mathcal{L}11}(x_{1}) $ $ {\bar{u}}_{\mathcal{L}21}(x_{1})=1-{\underline{u}}_{\mathcal{L}11}(x_{1}) $
Table 2.  Lower and upper membership functions of the observer
$ {\underline{u}}_{\mathcal{V}11}(x_{1})=e^{-\frac{x_{1}^{2}}{0.4}} $ $ {\bar{ u}}_{\mathcal{V}11}(x_{1})=e^{-\frac{x_{1}^{2}}{0.4}} $
$ {\underline{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V} 11}(x_{1}) $ $ {\bar{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V }11}(x_{1}) $
$ {\underline{u}}_{\mathcal{V}11}(x_{1})=e^{-\frac{x_{1}^{2}}{0.4}} $ $ {\bar{ u}}_{\mathcal{V}11}(x_{1})=e^{-\frac{x_{1}^{2}}{0.4}} $
$ {\underline{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V} 11}(x_{1}) $ $ {\bar{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V }11}(x_{1}) $
Table 3.  Lower and upper membership functions of the system
$ {\underline{u}}_{\mathcal{L}11}(x_{1})=\frac{\bar{e}_{\max }-\bar{e}}{\bar{e }_{\max }-\bar{e}_{\min }},\partial=0.03 $ $ {\bar{u}}_{\mathcal{L} 11}(x_{1})=\frac{\bar{e}_{\max }-\bar{e}}{\bar{e}_{\max }-\bar{e}_{\min }} ,\partial=0.01 $
$ {\underline{u}}_{\mathcal{L}21}(x_{1})=\frac{\bar{e}-\bar{e}_{\min}}{\bar{e} _{\max }-\bar{e}_{\min }},\partial=0.01 $ $ {\bar{u}}_{\mathcal{L}21}(x_{1})= \frac{\bar{e}-\bar{e}_{\min}}{\bar{e}_{\max }-\bar{e}_{\min }},\partial=0.03 $
$ {\underline{u}}_{\mathcal{L}11}(x_{1})=\frac{\bar{e}_{\max }-\bar{e}}{\bar{e }_{\max }-\bar{e}_{\min }},\partial=0.03 $ $ {\bar{u}}_{\mathcal{L} 11}(x_{1})=\frac{\bar{e}_{\max }-\bar{e}}{\bar{e}_{\max }-\bar{e}_{\min }} ,\partial=0.01 $
$ {\underline{u}}_{\mathcal{L}21}(x_{1})=\frac{\bar{e}-\bar{e}_{\min}}{\bar{e} _{\max }-\bar{e}_{\min }},\partial=0.01 $ $ {\bar{u}}_{\mathcal{L}21}(x_{1})= \frac{\bar{e}-\bar{e}_{\min}}{\bar{e}_{\max }-\bar{e}_{\min }},\partial=0.03 $
Table 4.  Lower and upper membership functions of the observer
$ {\underline{u}}_{\mathcal{V}11}(x_{1})=0.4e^{-\frac{x_{1}^{2}}{1.2}} $ $ { \bar{u}}_{\mathcal{V}11}(x_{1})=0.4e^{-\frac{x_{1}^{2}}{1.2}} $
$ {\underline{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V} 11}(x_{1}) $ $ {\bar{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V }11}(x_{1}) $
$ {\underline{u}}_{\mathcal{V}11}(x_{1})=0.4e^{-\frac{x_{1}^{2}}{1.2}} $ $ { \bar{u}}_{\mathcal{V}11}(x_{1})=0.4e^{-\frac{x_{1}^{2}}{1.2}} $
$ {\underline{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V} 11}(x_{1}) $ $ {\bar{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V }11}(x_{1}) $
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