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April  2021, 14(4): 1395-1414. doi: 10.3934/dcdss.2020379

Event-triggered adaptive fault-tolerant control for multi-agent systems with unknown disturbances

1. 

School of Automation and Guangdong Provincial Key Laboratory of Intelligent, Decision and Cooperative Control, Guangdong University of Technology, Guangzhou 510006, China

2. 

College of Engineering, Bohai University, Jinzhou 121013, China

* Corresponding author: Shubo Li

Received  January 2020 Revised  February 2020 Published  April 2021 Early access  May 2020

This paper presents an event-triggered consensus control protocol for a class of multi-agent systems with actuator faults, sensor faults and unknown disturbances. The adaptive neural network compensation control method is introduced to solve the problem of sensor faults. The event-triggered mechanism is developed to reduce the communication burden. In the control design process, the radial basis function neural networks are used to approximate the unknown nonlinear functions, and a nonlinear disturbance observer is used to eliminate the effect of unknown external disturbances. Furthermore, based on the graph theory and Lyapunov stability theory, it is further shown that the consensus tracking errors are semi-globally uniformly ultimately bounded. Finally, the simulation example illustrates the effectiveness of the designed control protocol.

Citation: Hongru Ren, Shubo Li, Changxin Lu. Event-triggered adaptive fault-tolerant control for multi-agent systems with unknown disturbances. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1395-1414. doi: 10.3934/dcdss.2020379
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S. Luo and D. Ye, Adaptive double event-triggered control for linear multi-agent systems with actuator faults, IEEE Transactions on Circuits and Systems I: Regular Papers, 66 (2019), 4829-4839.  doi: 10.1109/TCSI.2019.2932084.

[26]

Y. QianL. Liu and G. Feng, Output consensus of heterogeneous linear multi-agent systems with adaptive event-triggered control, IEEE Transactions on Automatic Control, 64 (2018), 2606-2613.  doi: 10.1109/TAC.2018.2868997.

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[30]

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[31]

Y. SuQ. Wang and C. Sun, Self-triggered consensus control for linear multi-agent systems with input saturation, IEEE/CAA Journal of Automatica Sinica, 7 (2020), 150-157.  doi: 10.1109/JAS.2019.1911837.

[32]

Y. SuB. ChenC. LinH. Wang and S. Zhou, Adaptive neural control for a class of stochastic nonlinear systems by backstepping approach, Information Sciences, 369 (2016), 748-764.  doi: 10.1016/j.ins.2016.06.010.

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[37]

X. WangS. LiX. Yu and J. Yang, Distributed active anti-disturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances, IEEE Transactions on Automatic Control, 62 (2017), 5795-5801.  doi: 10.1109/TAC.2016.2638966.

[38]

H. Wu and H. Su, Observer-based consensus for positive multiagent systems with directed topology and nonlinear control input, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49 (2018), 1459-1469.  doi: 10.1109/TSMC.2018.2852704.

[39]

Y. WuZ. WangS. Ding and H. Zhang, Leader–follower consensus of multi-agent systems in directed networks with actuator faults, Neurocomputing, 275 (2018), 1177-1185.  doi: 10.1016/j.neucom.2017.09.066.

[40]

G. Xie, L. Sun, T. Wen, X. Hei and F. Qian, Adaptive transition probability matrix-based parallel IMM algorithm, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 1–10. doi: 10.1109/TSMC.2019.2922305.

[41]

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.

[42]

F. YeB. SunL. Ou and W. Zhang, Disturbance observer-based control for consensus tracking of multi-agent systems with input delays from a frequency domain perspective, Systems & Control Letters, 114 (2018), 66-75.  doi: 10.1016/j.sysconle.2017.12.005.

[43]

Y. YeH. Su and Y. Sun, Event-triggered consensus tracking for fractional-order multi-agent systems with general linear models, Neurocomputing, 315 (2018), 292-298.  doi: 10.1016/j.neucom.2018.07.024.

[44]

X. YouC. Hua and X. Guan, Event-triggered leader-following consensus for nonlinear multiagent systems subject to actuator saturation using dynamic output feedback method, IEEE Transactions on Automatic Control, 63 (2018), 4391-4396.  doi: 10.1109/TAC.2018.2817160.

[45]

C. Zhang and G. Yang, Event-triggered adaptive output feedback control for a class of uncertain nonlinear systems with actuator failures, IEEE Transactions on Cybernetics, 50 (2018), 201-210.  doi: 10.1109/TCYB.2018.2868169.

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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.

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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.

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show all references

References:
[1]

A. BounemeurM. Chemachema and N. Essounbouli, Indirect adaptive fuzzy fault-tolerant tracking control for mimo nonlinear systems with actuator and sensor failures, ISA Transactions, 79 (2018), 45-61.  doi: 10.1016/j.isatra.2018.04.014.

[2]

L. Cao, H. Li, G. Dong and R. Lu, Event-triggered control for multiagent systems with sensor faults and input saturation, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 1–12. doi: 10.1109/TSMC.2019.2938216.

[3]

Z. Chen, Q.-L. Han, Y. Yan and Z. Wu, How often should one update control and estimation: Review of networked triggering techniques, SCIENCE CHINA Information Sciences, 63 (2020), 150201. doi: 10.1007/s11432-019-2637-9.

[4]

P. Du, H. Liang, S. Zhao and C. K. Ahn, Neural-based decentralized adaptive finite-time control for nonlinear large-scale systems with time-varying output constraints, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 1–12. doi: 10.1109/TSMC.2019.2918351.

[5]

Z. HouL. Cheng and M. Tan, Decentralized robust adaptive control for the multiagent system consensus problem using neural networks, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 39 (2009), 636-647.  doi: 10.1109/TSMCB.2008.2007810.

[6]

J. HuY. WuT. Li and B. K. Ghosh, Consensus control of general linear multiagent systems with antagonistic interactions and communication noises, IEEE Transactions on Automatic Control, 64 (2018), 2122-2127.  doi: 10.1109/TAC.2018.2872197.

[7]

W. HuL. Liu and G. Feng, Consensus of linear multi-agent systems by distributed event-triggered strategy, IEEE Transactions on Cybernetics, 46 (2016), 148-157.  doi: 10.1109/TCYB.2015.2398892.

[8]

W. HuL. Liu and G. Feng, Event-triggered cooperative output regulation of linear multi-agent systems under jointly connected topologies, IEEE Transactions on Automatic Control, 64 (2019), 1317-1322.  doi: 10.1109/TAC.2018.2849587.

[9]

C. HuaK. Li and X. Guan, Leader-following output consensus for high-order nonlinear multiagent systems, IEEE Transactions on Automatic Control, 64 (2018), 1156-1161.  doi: 10.1109/TAC.2018.2836024.

[10]

M. Hui, L. Hongyi, L. Renquan and T. Huang, Adaptive event-triggered control for a class of nonlinear systems with periodic disturbances, SCIENCE CHINA Information Sciences, 63 (2020), 150212. doi: 10.1007/s11432-019-2680-1.

[11]

J. LengH. ZhangD. YanQ. LiuX. Chen and D. Zhang, Digital twin-driven manufacturing cyber-physical system for parallel controlling of smart workshop, Journal of Ambient Intelligence and Humanized Computing, 10 (2019), 1155-1166.  doi: 10.1007/s12652-018-0881-5.

[12]

X. LiD. W. Ho and J. Cao, Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica, 99 (2019), 361-368.  doi: 10.1016/j.automatica.2018.10.024.

[13]

X. Li and S. Song, Stabilization of delay systems: Delay-dependent impulsive control, IEEE Transactions on Automatic Control, 62 (2017), 406-411.  doi: 10.1109/TAC.2016.2530041.

[14]

X. Li and J. Wu, Stability of nonlinear differential systems with state-dependent delayed impulses, Automatica, 64 (2016), 63-69.  doi: 10.1016/j.automatica.2015.10.002.

[15]

X. LiX. Yang and S. Song, Lyapunov conditions for finite-time stability of time-varying time-delay systems, Automatica, 103 (2019), 135-140.  doi: 10.1016/j.automatica.2019.01.031.

[16]

Y. Li and G. Yang, Adaptive fuzzy decentralized control for a class of large-scale nonlinear systems with actuator faults and unknown dead zones, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47 (2016), 729-740.  doi: 10.1109/TSMC.2016.2521824.

[17]

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.

[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]

Q. LiuH. ZhangJ. Leng and X. Chen, Digital twin-driven rapid individualised designing of automated flow-shop manufacturing system, International Journal of Production Research, 57 (2019), 3903-3919.  doi: 10.1080/00207543.2018.1471243.

[20]

Y. LiuX. LiuY. JingX. Chen and J. Qiu, Direct adaptive preassigned finite-time control with time-delay and quantized input using neural network, IEEE Transactions on Neural Networks and Learning Systems, 31 (2020), 1222-1231.  doi: 10.1109/TNNLS.2019.2919577.

[21]

Q. Liu, J. Leng, D. Yan, D. Zhang, L. Wei, A. Yu, R. Zhao, H. Zhang and X. Chen, Digital twin-based designing of the configuration, motion, control, and optimization model of a flow-type smart manufacturing system, Journal of Manufacturing Systems, 2020, 1–13. doi: 10.1016/j.jmsy.2020.04.012.

[22]

Y. LiuX. LiuY. Jing and Z. Zhang, A novel finite-time adaptive fuzzy tracking control scheme for nonstrict feedback systems, IEEE Transactions on Fuzzy Systems, 27 (2018), 646-658.  doi: 10.1109/TFUZZ.2018.2866264.

[23]

R. LuY. XuA. Xue and J. Zheng, Networked control with state reset and quantized measurements: Observer-based case, IEEE Transactions on Industrial Electronics, 60 (2012), 5206-5213.  doi: 10.1109/TIE.2012.2227910.

[24]

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.

[25]

S. Luo and D. Ye, Adaptive double event-triggered control for linear multi-agent systems with actuator faults, IEEE Transactions on Circuits and Systems I: Regular Papers, 66 (2019), 4829-4839.  doi: 10.1109/TCSI.2019.2932084.

[26]

Y. QianL. Liu and G. Feng, Output consensus of heterogeneous linear multi-agent systems with adaptive event-triggered control, IEEE Transactions on Automatic Control, 64 (2018), 2606-2613.  doi: 10.1109/TAC.2018.2868997.

[27]

W. Ren, Distributed attitude alignment in spacecraft formation flying, Internat. J. Adapt. Control Signal Process., 21 (2007), 95-113.  doi: 10.1002/acs.916.

[28]

R. O. Saber and R. M. Murray, Consensus protocols for networks of dynamic agents, 2003 American Control Conference, 2 (2003), 951-956.  doi: 10.1109/ACC.2003.1239709.

[29]

R. SakthivelA. ParivallalB. KaviarasanH. Lee and Y. Lim, Finite-time consensus of Markov jumping multi-agent systems with time-varying actuator faults and input saturation, ISA Transactions, 83 (2018), 89-99.  doi: 10.1016/j.isatra.2018.08.016.

[30]

R. SakthivelR. SakthivelB. KaviarasanH. Lee and Y. Lim, Finite-time leaderless consensus of uncertain multi-agent systems against time-varying actuator faults, Neurocomputing, 325 (2019), 159-171.  doi: 10.1016/j.neucom.2018.10.020.

[31]

Y. SuQ. Wang and C. Sun, Self-triggered consensus control for linear multi-agent systems with input saturation, IEEE/CAA Journal of Automatica Sinica, 7 (2020), 150-157.  doi: 10.1109/JAS.2019.1911837.

[32]

Y. SuB. ChenC. LinH. Wang and S. Zhou, Adaptive neural control for a class of stochastic nonlinear systems by backstepping approach, Information Sciences, 369 (2016), 748-764.  doi: 10.1016/j.ins.2016.06.010.

[33]

D. Sumpter and S. Pratt, A modelling framework for understanding social insect foraging, Behavioral Ecology and Sociobiology, 53 (2003), 131-144.  doi: 10.1007/s00265-002-0549-0.

[34]

X. TanJ. Cao and X. Li, Consensus of leader-following multiagent systems: A distributed event-triggered impulsive control strategy, IEEE Transactions on Cybernetics, 49 (2018), 792-801.  doi: 10.1109/TCYB.2017.2786474.

[35]

A. WangX. Liao and T. Dong, Fractional-order follower observer design for tracking consensus in second-order leader multi-agent systems: Periodic sampled-based event-triggered control, Journal of the Franklin Institute, 355 (2018), 4618-4628.  doi: 10.1016/j.jfranklin.2018.01.036.

[36]

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.

[37]

X. WangS. LiX. Yu and J. Yang, Distributed active anti-disturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances, IEEE Transactions on Automatic Control, 62 (2017), 5795-5801.  doi: 10.1109/TAC.2016.2638966.

[38]

H. Wu and H. Su, Observer-based consensus for positive multiagent systems with directed topology and nonlinear control input, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49 (2018), 1459-1469.  doi: 10.1109/TSMC.2018.2852704.

[39]

Y. WuZ. WangS. Ding and H. Zhang, Leader–follower consensus of multi-agent systems in directed networks with actuator faults, Neurocomputing, 275 (2018), 1177-1185.  doi: 10.1016/j.neucom.2017.09.066.

[40]

G. Xie, L. Sun, T. Wen, X. Hei and F. Qian, Adaptive transition probability matrix-based parallel IMM algorithm, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 1–10. doi: 10.1109/TSMC.2019.2922305.

[41]

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.

[42]

F. YeB. SunL. Ou and W. Zhang, Disturbance observer-based control for consensus tracking of multi-agent systems with input delays from a frequency domain perspective, Systems & Control Letters, 114 (2018), 66-75.  doi: 10.1016/j.sysconle.2017.12.005.

[43]

Y. YeH. Su and Y. Sun, Event-triggered consensus tracking for fractional-order multi-agent systems with general linear models, Neurocomputing, 315 (2018), 292-298.  doi: 10.1016/j.neucom.2018.07.024.

[44]

X. YouC. Hua and X. Guan, Event-triggered leader-following consensus for nonlinear multiagent systems subject to actuator saturation using dynamic output feedback method, IEEE Transactions on Automatic Control, 63 (2018), 4391-4396.  doi: 10.1109/TAC.2018.2817160.

[45]

C. Zhang and G. Yang, Event-triggered adaptive output feedback control for a class of uncertain nonlinear systems with actuator failures, IEEE Transactions on Cybernetics, 50 (2018), 201-210.  doi: 10.1109/TCYB.2018.2868169.

[46]

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Figure 1.  Topology of communication graph
Figure 2.  Output trajectories of followers and the leader
Figure 3.  The trajectories of tracking errors
Figure 4.  The trajectories of event-triggered controllers
Figure 5.  The trajectories of errors between disturbances and disturbance observers
Figure 6.  The trajectories of errors between disturbances and disturbance observers
Figure 7.  Triggering instants and inter-event intervals
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