多智能体系统周期动态事件触发二分一致性

doi:10.12305/j.issn.1001-506X.2026.01.25

摘要/Abstract

摘要：

针对一般线性多智能体系统资源受限条件下的领导-跟随二分一致性问题，基于改进周期动态事件触发机制设计了一种低通信成本的控制协议，其中个体控制器通过邻居及自身估计误差自适应调节其控制输入，同时通过引入指数项增大周期动态事件的触发阈值，然后利用Lyapunov方法得到了系统可解二分一致性的充分性条件。仿真结果表明，相较于周期动态事件触发机制，该机制在不影响系统的收敛速度的前提下，系统整体触发次数减少了49%；当领导-跟随误差小于±0.3时，触发次数减少了92.1%。由此可见，所提方法显著降低了多智能体之间的通信成本，对于大规模网络化系统一致性问题的物理实现具有重要现实意义。

关键词: 多智能体系统, 周期动态事件触发, 领导-跟随一致性, 二分一致性, 自适应控制

Abstract:

In view of the leader-following bipartite consensus problem in general linear multi-agent systems with resource constraints, a control protocol with low communication cost is proposed based on an improved dynamic periodic event-triggered mechanism, in which the individual controllers adaptively adjust the control input only depending on neighbors and its own estimation error, and the threshold of dynamic periodic event-triggered mechanism is increased by incorporating an exponential term. Then, a sufficient condition is derived by Lyapunov method for the system to solve the considered bipartite consensus problem. Simulation results show that compared with the dynamic periodic event-triggered mechanism, the proposed mechanism reduces the overall number of systems triggering events by 49% while maintaining the same convergence rate of the system. Meanwhile, the number of triggers is reduced by 92.1% as the leader-following error is less than ±0.3. In this sense, the proposed method significantly reduces the communication cost of multi-agent systems, which is important for the practical implementation of consensus problem in large-scale networked systems.

Key words: multi-agent systems, dynamic periodic event-triggered, leader-following consensus, bipartite consensus, adaptive control

中图分类号:

TP 273

李宗刚, 邱进涛, 宁小刚, 陈引娟. 多智能体系统周期动态事件触发二分一致性[J]. 系统工程与电子技术, 2026, 48(1): 278-289.

Zonggang LI, Jintao QIU, Xiaogang NING, Yinjuan CHEN. Dynamic periodic event-triggered bipartite consensus for multi-agent systems[J]. Systems Engineering and Electronics, 2026, 48(1): 278-289.

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参考文献 34

1	余世明, 周景远, 何德峰, 等. 随机有界通信时延下传感器网络中的一致性时钟同步算法[J]. 控制与决策, 2020, 35 (5): 1159- 1166.
	YU S M, ZHOU J Y, HE D F, et al. Time synchronization based on consensus in WSN with random bounded communication delay[J]. Control and Decision, 2020, 35 (5): 1159- 1166.
2	王长城, 戚国庆, 李银伢, 等. 传感器网络一致性分布式滤波算法[J]. 控制理论与应用, 2012, 29 (12): 1645- 1650.
	WANG C C, QI G Q, LI Y Y, et al. Consensus-based distributed ﬁltering algorithm in sensor networks[J]. Control Theory & Applications, 2012, 29 (12): 1645- 1650.
3	CHEN W, LIU G P. Privacy-preserving consensus- based distributed economic dispatch of smart grids via state decomposition[J]. IEEE/CAA Journal of Automatica Sinica, 2024, 11 (5): 1250- 1261. doi: 10.1109/JAS.2023.124122
4	LI K W, FENG K L, LI Y M. Fuzzy adaptive fault-tolerant formation control for USVs with intermittent actuator faults[J]. IEEE Trans. on Intelligent Vehicles, 2024, 9 (3): 4445- 4455. doi: 10.1109/TIV.2024.3358351
5	CAO X M, LI K W, LI Y M. Robust adaptive formation control for nonlinear multi-agent systems with range constraints[J]. Nonlinear Dynamics, 2024, 1123 (3): 1917- 1929.
6	杜同春, 王波, 程浩然, 等. 聚类与信息共享的多智能体深度强化学习协同控制交通灯[J]. 电子与信息学报, 2024, 46 (2): 538- 545.
	DU T C, WANG B, CHENG H R, et al. Multi-agent deep reinforcement learning with clustering and information sharing for traffic light cooperative control[J]. Journal of Electronics & Information Technology, 2024, 46 (2): 538- 545.
7	TABUADA P. Event-triggered real-time scheduling of stabilizing control tasks[J]. IEEE Trans. on Automatic Control, 2007, 52 (9): 1680- 1685. doi: 10.1109/TAC.2007.904277
8	ZHANG L M, SUN J, YANG Q K. Distributed model-based event-triggered leader-follower consensus control for linear continuous-time multiagent systems[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2020, 51 (10): 6457- 6465.
9	ZHANG J, ZHANG H G, CAI Y L, et al. Consensus control for nonlinear multi-agent systems with event-triggered communications[J]. Applied Mathematics and Computation, 2021, 408, 126341- 126357. doi: 10.1016/j.amc.2021.126341
10	CHENG Y. Fully distributed event-triggered leader-follower tracking control for multi-agent systems over directed switching networks[C]// Proc. of the 40th Chinese Control Conference, 2021: 5362−5366.
11	LUO Y P, PANG J L. Observer-based event-triggered finite-time consensus for general linear leader-follower multi-agent systems[J]. Advances in Continuous and Discrete Models, 2022, 2022 (1): 40- 57. doi: 10.1186/s13662-022-03711-x
12	SUN Y, PENG S. Consensus of discrete-time leader-following linear multi-agent systems under lyapunov-function-based event-triggered mechanism[J]. IEEE Trans. on Circuits and Systems II: Express Briefs, 2023, 70 (12): 4409- 4413.
13	张国庆, 徐轶晖, 李纪强, 等. 基于异步搜寻制导的机/船协同事件触发控制[J]. 系统工程与电子技术, 2025, 47 (9): 3058- 3065.
	ZHANG G Q, XU Y H, LI J Q, et al. Event-triggered control for USV/UAV based on asynchronous search guidance[J]. Systems Engineering and Electronics, 2025, 47 (9): 3058- 3065.
14	GIRARD A. Dynamic triggering mechanisms for event-triggered control[J]. IEEE Trans. on Automatic Control, 2014, 60 (7): 1992- 1997.
15	TARBOURIECH S, GIRARD A. LMI-based design of dynamic event-triggering mechanism for linear systems[C]//Proc. of the IEEE Conference on Decision and Control, 2018: 121−126.
16	HU S W, QIU J L, CHEN X Y, et al. Dynamic event-triggered control for leader-following consensus of multiagent systems with the estimator[J]. IET Control Theory & Applications, 2022, 16 (4): 475- 484.
17	CHEN J J, CHEN B S, ZENG Z G. Leader- following consensus of linear multi-agent systems via dynamic event-triggered adjustable control protocol[C]//Proc. of the IEEE 14th International Conference on Advanced Computational Intelligence, 2022: 21−28.
18	RUAN X L, FENG J W, XU C, et al. Observer-based dynamic event-triggered strategies for leader-following consensus of multi-agent systems with disturbances[J]. IEEE Trans. on Network Science and Engineering, 2020, 7 (4): 3148- 3158. doi: 10.1109/TNSE.2020.3017493
19	YANG R H, SU X W, ZHANG S X, et al. Simultaneous fault detection and leader-following consensus for multiagent systems with directed graphs via dynamic event-triggered strategy[J]. IEEE Trans. on Instrumentation and Measurement, 2023, 72, 1- 11.
20	ZHANG J, ZHANG H G, WANG W, et al. Adaptive dynamic event-triggered distributed output observer for leader-follower multiagent systems under directed graphs[J]. IEEE Trans. on Neural Networks and Learning Systems, 2024, 35 (12): 17440- 17449.
21	LUO S P, YE D. Double event-triggered control for linear multi-agent systems with augmented dynamic triggering mechanisms[J]. Applied Mathematics and Computation, 2020, 386, 125522- 125536. doi: 10.1016/j.amc.2020.125522
22	GUAN J C, REN H W, TAN G L. Distributed dynamic event-triggered control to leader-following consensus of nonlinear multi-agent systems with directed graphs[J]. Entropy, 2024, 26 (2): 113- 127. doi: 10.3390/e26020113
23	LIU X, HE S H, WU Y Q. Distributed dynamic event-triggered leader-following consensus for nonlinear multiagent systems over fading channel[J]. IEEE Trans. on Cybernetics, 2023, 54 (8): 4593- 4602.
24	范泉涌, 张乃宗, 唐勇, 等. 基于动态事件触发通信协议的多智能体系统自适应可靠控制[J]. 自动化学报, 2024, 50 (5): 924- 936. doi: 10.16383/j.aas.c230766
	FAN Q Y, ZHANG N Z, TANG Y, et al. Adaptive reliable control of multi-agent systems based on dynamic event-triggered communication protocol[J]. Acta Automatica Sinica, 2024, 50 (5): 924- 936. doi: 10.16383/j.aas.c230766
25	HEEMELS W, DONKERS M C F, TEEL A R. Periodic event-triggered control based on state feedback[C]//Proc. of the IEEE 50th Conference on Decision and Control and European Control Conference, 2011: 2571−2576.
26	LI S, CHEN Y, LIU P X. Double event-triggered leader-following consensus and fault detection for Lipschitz nonlinear multi-agent systems via periodic sampling strategy[J]. Nonlinear Dynamics, 2023, 111 (9): 8293- 8311. doi: 10.1007/s11071-023-08268-2
27	LIN N, LING Q. Dynamic periodic event-triggered consensus protocols for linear multiagent systems with network delay[J]. IEEE Systems Journal, 2022, 17 (1): 1204- 1215.
28	LI C C, ZHAO X D, CHEN M, et al. Dynamic periodic event-triggered control for networked control systems under packet dropouts[J]. IEEE Trans. on Automation Science and Engineering, 2023, 21 (1): 906- 920.
29	ZHENG S Q, LI Z P, ZHAI C, et al. Periodic event-triggered secure consensus for networked mechanical systems under denial-of-service attacks[J]. Control Theory and Technology, 2024, 22 (1): 1- 13. doi: 10.1007/s11768-023-00182-7
30	WANG W X, YE H T, LUO W G, et al. Asymmetric bipartite consensus of multi-agent systems under periodic detection event-triggered mechanism[J]. Electronics, 2022, 11 (13): 2036- 2050. doi: 10.3390/electronics11132036
31	QI Y N, MU R, ZHANG X F. Periodic event-triggered bipartite consensus for multi-agent systems with partial information transmission[J]. Asian Journal of Control, 2022, 24 (5): 2778- 2786. doi: 10.1002/asjc.2648
32	CAI Y L, WANG Y C, LI W H, et al. Distributed bipartite consensus of linear multi-agent systems based on periodic event-triggered mechanism[J]. International Journal of Robust and Nonlinear Control, 2023, 33 (10): 5775- 5799. doi: 10.1002/rnc.6668
33	WU X J, DING S, XU N, et al. Periodic event-triggered bipartite containment control for nonlinear multi-agent systems with input delay[J]. International Journal of Systems Science, 2024, 55 (10): 2008- 2022. doi: 10.1080/00207721.2024.2328780
34	SLOTINE J J E, LI W. Applied nonlinear control [M]. Englewood Cliffs: Prentice Hall, 1991.

触发条件	智能体1	智能体2	智能体3	智能体4	智能体5
式（15）	140	139	153	83	58
式（48）	288	335	365	180	101

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