于镝 , 王亚洁 , 赵博 , 等 . 动态事件触发机制下多智能体系统固定时间跟踪 [J ] . 兵工学报 , 2023 , 44 ( 5 ): 1403 - 1413 .

YU D , WANG Y J , ZHAO B , et al. Fixed-time tracking control of multi-agent systems under dynamic event-triggering mechanism [J ] . Acta Armamentarii , 2023 , 44 ( 5 ): 1403 - 1413 . (in Chinese) DOI: 10.12382/bgxb.2022.1267 http://doi.org/10.12382/bgxb.2022.1267 To solve the tracking control problem of disturbed nonlinear multi-agent system, a fixed-time integral sliding mode control method is proposed based on dynamic event triggering mechanism. A new integral sliding mode surface is designed based on relative state information, the distributed control protocol is developed, and dynamic variable and dynamic event triggering mechanism are constructed on the basis of the measurement error and the sliding mode surface. It can be proved that the appropriate selection of control parameters can drive the multi-agent system to achieve trajectory tracking within a fixed time under the dynamic event triggering mechanism with Zeno behavior avoided. The proposed control scheme can effectively suppress the influence of system disturbance and reduce the consumption of communication and computing resources of the multi-agent system, and meanwhile, avoid the dependence of the convergence time on the initial states of the system. The simulation results demonstrate that the proposed dynamic event triggering controller allows the multi-agent system to achieve the tracking control in fixed time and reduce the triggering frequency to save resources, which is more suitable for practical applications.

张栋 , 马苏慧 , 吕石 , 等 . 多智能体系统事件触发一致性研究综述 [J ] . 北京理工大学学报 , 2022 , 42 ( 10 ): 1059 - 1072 .

ZHANG D , MA S H , LÜ S , et al. A survey of event-triggered consensus for multi-agent systems [J ] . Transactions of Beijing Institute of Technology , 2022 , 42 ( 10 ): 1059 - 1072 . (in Chinese)

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ZHAO G L , HUA C C , GUAN X P . Distributed event-triggered consensus of multiagent systems with communication delays: a hybrid system approach [J ] . IEEE Transactions on Cybernetics , 2019 , 50 ( 7 ): 3169 - 3181 . DOI: 10.1109/TCYB.6221036 http://doi.org/10.1109/TCYB.6221036 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6221036 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6221036

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LIU J , ZHANG Y L , SUN C Y , et al. Fixed-time consensus of multi-agent systems with input delay and uncertain disturbances via event-triggered control [J ] . Information Sciences , 2019 , 480 : 261 - 272 . DOI: 10.1016/j.ins.2018.12.037 http://doi.org/10.1016/j.ins.2018.12.037 https://linkinghub.elsevier.com/retrieve/pii/S0020025518309988 https://linkinghub.elsevier.com/retrieve/pii/S0020025518309988

RAN G T , LIU J , LI C J , et al. Event-based finite-time consensus control of second-order delayed multi-agent systems [J ] . IEEE Transactions on Circuits and Systems II: Express Briefs , 2020 , 68 ( 1 ): 276 - 280 .

PIAN Y , CARLO F , DIMOS V D . Distributed event-triggered communication and control of linear multiagent systems under tactile communication [J ] . IEEE Transactions on Automatic Control , 2018 , 63 ( 11 ): 3979 - 3985 . DOI: 10.1109/TAC.9 http://doi.org/10.1109/TAC.9 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9

LI L , HUANG M . Event-triggered consensus control for singular multi-agent systems based on observers [J ] . Transactions of the Institute of Measurement and Control , 2023 , 45 ( 9 ): 1661 - 1672 . DOI: 10.1177/01423312221138887 http://doi.org/10.1177/01423312221138887 http://journals.sagepub.com/doi/10.1177/01423312221138887 http://journals.sagepub.com/doi/10.1177/01423312221138887 This paper is devoted to the problem of event-triggered consensus for a class of general linear singular multi-agent systems with undirected topology. Considering that the system states are not measurable, state observers are designed first, and then a new observer-based event-triggered sampling mechanism is proposed, which naturally avoids Zeno behavior. Furthermore, a distributed event-triggered consensus protocol is designed. By employing the Lyapunov-Krasovskii functional method and model transformation approach, sufficient conditions are obtained such that the consensus of the singular multi-agent systems can be achieved, while the explicit dynamic expression of the consensus function is also given. Finally, a numerical example is included to illustrate the effectiveness of the proposed results.

XUE S S , LI H , CAO H , et al. Distributed edge-event-triggered consensus of multi-agent system under DoS attack [J ] . Pattern Recognition Letters , 2023 , 174 : 118 - 123 . DOI: 10.1016/j.patrec.2023.08.015 http://doi.org/10.1016/j.patrec.2023.08.015 https://linkinghub.elsevier.com/retrieve/pii/S0167865523002362 https://linkinghub.elsevier.com/retrieve/pii/S0167865523002362

YUAN F , FENG G , WANG Y , et al. Distributed event-triggered control of multi-agent systems with combinational measurements [J ] . Automatica , 2013 , 49 ( 2 ): 671 - 675 . DOI: 10.1016/j.automatica.2012.11.010 http://doi.org/10.1016/j.automatica.2012.11.010 https://linkinghub.elsevier.com/retrieve/pii/S0005109812005468 https://linkinghub.elsevier.com/retrieve/pii/S0005109812005468

CHENG T H , KAN Z , KLOTZ J R , et al. Event-triggered control of multiagent systems for fixed and time-varying network topologies [J ] . IEEE Transactions on Automatic Control , 2017 , 62 ( 10 ): 5365 - 5371 . DOI: 10.1109/TAC.2017.2693824 http://doi.org/10.1109/TAC.2017.2693824 http://ieeexplore.ieee.org/document/7898365/ http://ieeexplore.ieee.org/document/7898365/

ZUO Z Y , KE R Q , HAN Q L . Fully distributed adaptive practical fixed-time consensus protocols for multi-agent systems [J ] . Automatica , 2023 , 157 : 111248 . DOI: 10.1016/j.automatica.2023.111248 http://doi.org/10.1016/j.automatica.2023.111248 https://linkinghub.elsevier.com/retrieve/pii/S0005109823004090 https://linkinghub.elsevier.com/retrieve/pii/S0005109823004090

REN W H , ZHANG X X . Fully distributed containment control of second-order nonlinear multi-agent systems using disturbance observer with directed graph [J ] . Information Sciences , 2023 , 649 : 119629 . DOI: 10.1016/j.ins.2023.119629 http://doi.org/10.1016/j.ins.2023.119629 https://linkinghub.elsevier.com/retrieve/pii/S0020025523012148 https://linkinghub.elsevier.com/retrieve/pii/S0020025523012148

FRANCESCHELLI M , GASPARRI A , GIUA A , et al. Decentralized estimation of Laplacian eigenvalues in multi-agent systems [J ] . Automatica , 2013 , 49 ( 4 ): 1031 - 1036 . DOI: 10.1016/j.automatica.2013.01.029 http://doi.org/10.1016/j.automatica.2013.01.029 https://linkinghub.elsevier.com/retrieve/pii/S0005109813000307 https://linkinghub.elsevier.com/retrieve/pii/S0005109813000307

YANG D , REN W , LIU X , et al. Decentralized event-triggered consensus for linear multi-agent systems under general directed graphs [J ] . Automatica , 2016 , 69 : 242 - 249 . DOI: 10.1016/j.automatica.2016.03.003 http://doi.org/10.1016/j.automatica.2016.03.003 https://linkinghub.elsevier.com/retrieve/pii/S0005109816300826 https://linkinghub.elsevier.com/retrieve/pii/S0005109816300826

CHENG B , LI Z K . Fully distributed event triggered protocols for linear multiagent networks [J ] . IEEE Transactions on Automatic Control , 2018 , 64 ( 4 ): 1655 - 1662 . DOI: 10.1109/TAC.9 http://doi.org/10.1109/TAC.9 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9

XU W , HE W , HO D W C , et al. Fully distributed observer-based consensus protocol: adaptive dynamic event-triggered schemes [J ] . Automatica , 2022 , 139 : 110188 . DOI: 10.1016/j.automatica.2022.110188 http://doi.org/10.1016/j.automatica.2022.110188 https://linkinghub.elsevier.com/retrieve/pii/S0005109822000334 https://linkinghub.elsevier.com/retrieve/pii/S0005109822000334

LIU X P , SONG J B , ZHANG X X . Fully distributed leader-follower consensus for multi-agent systems based on reduced-order adaptive feedback protocol [J ] . Transactions of the Institute of Measurement and Control , 2023 , 45 ( 13 ): 2526 - 2535 . DOI: 10.1177/01423312231156665 http://doi.org/10.1177/01423312231156665 http://journals.sagepub.com/doi/10.1177/01423312231156665 http://journals.sagepub.com/doi/10.1177/01423312231156665 This paper addresses the leader–follower consensus problem of linear multi-agent systems by designing reduced-order adaptive output feedback protocol. Using relative output information among neighboring agents, node-based adaptive output feedback control protocol and edge-based adaptive output feedback control protocol are presented, respectively. For both cases, based on Lyapunov analysis and algebraic Riccati equation design, some sufficient conditions are given to achieve leader–follower consensus by applying the proposed adaptive output feedback protocols. Finally, some simulation examples are given to illustrate the validity of the theoretical results.

HU W F , YANG C H , HUANG T W , et al. A distributed dynamic event-triggered control approach to consensus of linear multiagent systems with directed networks [J ] . IEEE Transactions on Cybernetics , 2018 , 50 ( 2 ): 869 - 874 . DOI: 10.1109/TCYB.6221036 http://doi.org/10.1109/TCYB.6221036 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6221036 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6221036

ZHAO G L , WEI H , FU X . Distributed dynamic event-triggered control approach to multi-agent systems via adaptive consensus protocols [J ] . Asian Journal of Control , 2022 , 24 ( 3 ): 1486 - 1496 . DOI: 10.1002/asjc.v24.3 http://doi.org/10.1002/asjc.v24.3 https://onlinelibrary.wiley.com/toc/19346093/24/3 https://onlinelibrary.wiley.com/toc/19346093/24/3

HEEMELS W P M H , DONKERS M C F , Teel A R . Periodic event-triggered control for linear systems [J ] . IEEE Transactions on Automatic Control , 2012 , 58 ( 4 ): 847 - 861 . DOI: 10.1109/TAC.2012.2220443 http://doi.org/10.1109/TAC.2012.2220443 http://ieeexplore.ieee.org/document/6310015/ http://ieeexplore.ieee.org/document/6310015/

SUN J , GUO C , LIU L , et al. Adaptive consensus control of second-order nonlinear multi-agent systems with event-dependent intermittent communications [J ] . Journal of the Franklin Institute , 2023 , 360 ( 3 ): 2289 - 2306 . DOI: 10.1016/j.jfranklin.2022.10.045 http://doi.org/10.1016/j.jfranklin.2022.10.045 https://linkinghub.elsevier.com/retrieve/pii/S0016003222007724 https://linkinghub.elsevier.com/retrieve/pii/S0016003222007724

SUN J , GUO C , SHAN Q H , et al. Consensus of multi-agent systems with state-dependent intermittent communication [J ] . Transactions of the Institute of Measurement and Control , 2023 , 45 ( 11 ): 2070 - 2080 . DOI: 10.1177/01423312221147948 http://doi.org/10.1177/01423312221147948 http://journals.sagepub.com/doi/10.1177/01423312221147948 http://journals.sagepub.com/doi/10.1177/01423312221147948 This paper deals with the consensus control problem for a class of multi-agent systems with state-dependent intermittent communication. The main contribution is that a novel state-dependent intermittent scheme is proposed, where whether the control protocols are implemented on the agents or not is related to system dynamics. In this communication scheme, by dividing the nonnegative real region into three subregions, the work time and the rest time are dependent on the pre-given subregions and a function value describing the error state. Based on this, a novel state-dependent intermittent control protocol can be designed and the sufficient conditions for the overall consensus can further be obtained. Compared to the existing time-dependent intermittent communication schemes, the proposed state-dependent one can tolerate more rest time. Finally, two simulation examples are developed to illustrate our results.

ZHANG H , QIU J B , YAN H C , et al. An estimator-based dynamic event-triggered protocol for linear multiagent systems [J ] . IEEE Control Systems Letters , 2022 , 6 : 2629 - 2634 . DOI: 10.1109/LCSYS.2022.3172791 http://doi.org/10.1109/LCSYS.2022.3172791 https://ieeexplore.ieee.org/document/9769691/ https://ieeexplore.ieee.org/document/9769691/

YANG Y Q , GE M F , LIANG C D , et al. Predefined-time formation control of NASVs with fully discontinuous communication: a novel hierarchical event-triggered scheme [J ] . Ocean Engineering , 2023 , 268 : 113422 . DOI: 10.1016/j.oceaneng.2022.113422 http://doi.org/10.1016/j.oceaneng.2022.113422 https://linkinghub.elsevier.com/retrieve/pii/S0029801822027056 https://linkinghub.elsevier.com/retrieve/pii/S0029801822027056

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DU X N , QU S C , ZHANG H R , et al. Distributed bipartite consensus for multi-agent systems with dynamic event-triggered mechanism [J ] . Journal of the Franklin Institute , 2023 , 360 ( 12 ): 8877 - 8897 . DOI: 10.1016/j.jfranklin.2022.05.022 http://doi.org/10.1016/j.jfranklin.2022.05.022 https://linkinghub.elsevier.com/retrieve/pii/S0016003222003106 https://linkinghub.elsevier.com/retrieve/pii/S0016003222003106

XU W , HE W , HO D W C , et al. Fully distributed observer-based consensus protocol: adaptive dynamic event-triggered schemes [J ] . Automatica , 2022 , 139 : 110188 . DOI: 10.1016/j.automatica.2022.110188 http://doi.org/10.1016/j.automatica.2022.110188 https://linkinghub.elsevier.com/retrieve/pii/S0005109822000334 https://linkinghub.elsevier.com/retrieve/pii/S0005109822000334

邓甲 , 王付永 , 刘忠信 , 等 . 动态事件触发机制下二阶多智能体系统完全分布式控制 [J/OL ] . 控制理论与应用 , 2023 ( 2023-10-17 )[ 2023-11-26 ] . http://kns.cnki.net/kcms/detail/44.1240.TP.20230106.1723.01.html http://kns.cnki.net/kcms/detail/44.1240.TP.20230106.1723.01.html http://kns.cnki.net/kcms/detail/44.1240.TP.20230106.1723.01.html.

DENG J , WANG F Y , LIU Z X , et al. Fully distributed control of second-order multi-agent systems under dynamic event-triggered mechanism [J/OL ] . Control Theory & Application , 2023 ( 2023-10-17 ). (in Chinese)

WU Y , ZHANG H , WANG Z , et al. Distributed event-triggered consensus of general linear multiagent systems under directed graphs [J ] . IEEE Transactions on Cybernetics , 2020 , 52 ( 1 ): 608 - 619 . DOI: 10.1109/TCYB.2020.2981210 http://doi.org/10.1109/TCYB.2020.2981210 https://ieeexplore.ieee.org/document/9058973/ https://ieeexplore.ieee.org/document/9058973/