Fixed-Time Bipartite Consensus of Multi-agent Systems via Event-Triggered Control

doi:10.3778/j.issn.1002-8331.2010-0170

Abstract

Abstract:

The fixed-time bipartite consensus problem is investigated for first-order multi-agent systems with signed directed graphs. To reduce the energy consumption in the control process, a distributed event-triggered control protocol is proposed. With designed protocol, graph theory and Lyapunov theory are utilized to derive sufficient conditions for fixed-time bipartite consensus. The upper bound of the convergence time is also provided, which is independent of the initial conditions. In addition, it is shown that the proposed event-triggered control scheme can avoid the continuous control of the agents and the Zeno behavior effectively. Finally, numerical examples are provided to verify the validity of obtained theoretical results.

Key words: first-order multi-agent system, signed directed graph, event-triggered mechanism, fixed-time bipartite consensus

摘要：

针对具有符号有向图的一阶多智能体系统，研究了其固定时间二分一致性问题。为降低控制过程中多智能体系统的能量损耗，提出了一种基于事件触发机制的分布式控制协议。以图论和李雅普诺夫理论为主要研究工具，给出了多智能体系统在所设计控制协议作用下实现固定时间二分一致性的充分条件和与系统初始状态无关的收敛时间上界，并证明了使用该协议可以有效避免对智能体的连续控制和Zeno行为的发生。数值算例验证了所得理论结果的有效性。

关键词: 一阶多智能体系统, 符号有向图, 事件触发机制, 固定时间二分一致性

LI Zhentao, FENG Yuanzhen, WANG Zhengxin. Fixed-Time Bipartite Consensus of Multi-agent Systems via Event-Triggered Control[J]. Computer Engineering and Applications, 2021, 57(21): 80-86.

李振涛，冯元珍，王正新. 事件触发下多智能体系统固定时间二分一致性[J]. 计算机工程与应用, 2021, 57(21): 80-86.

References

[1] 熊涛，曹科才，柴运，等.基于输入约束一致性算法的多无人机编队控制[J].计算机工程与应用，2018，54（12）：51-56.
XIONG T，CAO K C，CHAI Y，et al.Consensus algorithm with input constraint based formation control for multiple UAVs[J].Computer Engineering and Applications，2018，54（12）：51-56，125.
[2] 张洪海，钱晓鹏，吴鑫炜，等.基于路径-速度解耦的无人机编队协同轨迹规划[J].系统工程与电子技术，2020，42（9）：1976-1987.
ZHANG H H，QIAN X P，WU X W，et al.Cooperative trajectory planning for UAV formation based on path-speed decoupling[J].Systems Engineering and Electronics，2020，42（9）：1976-1987.
[3] 冯智慧，宋春燕，张广洲，等.基于分布式多层体系的输变电工程电磁环境智能实时监测系统[J].Electric Power，2016，49（1）：109-113.
FENG Z H，SONG C Y，ZHANG G Z，et al.An intelligent real-time monitoring system for the power transmission electromagnetic environment based on a distributed multi-tier architecture[J].Electric Power，2016，49（1）：109-113.
[4] OLFATI-SABER R，FAX J A，MURRAY R M.Consensus and cooperation in networked multi-agent systems[J].Proceedings of the IEEE，2007，95（1）：215-233.
[5] NEDIC A，OZDAGLAR A，PARRILO P A.Constrained consensus and optimization in multi-agent networks[J].IEEE Transactions on Automatic Control，2010，55（4）：922-938.
[6] YU W W，CHEN G R，CAO M，et al.Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics[J].IEEE Transactions on Systems，Man，and Cybernetics，Part B，2010，40（3）：881-891.
[7] SONG Q，CAO J D，YU W W.Second-order leader-following consensus of nonlinear multi-agent systems via pinning control[J].Systems & Control Letters，2010，59（9）：553-562.
[8] HUANG J.The consensus for discrete-time linear multi-agent systems under directed switching networks[J].IEEE Transactions on Automatic Control，2017，62（8）：4086-4092.
[9] BHAT S P，BERNSTEIN D S.Finite-time stability of continuous autonomous systems[J].SIAM Journal on Control and Optimization，2000，38（3）：751-766.
[10] LIN X，ZHENG Y S.Finite-time consensus of switched multiagent Systems[J].IEEE Transactions on Systems，Man，and Cybernetics：Systems，2017，47（7）：1535-1545.
[11] SHI S，FENG H Y，LIU W H，et al.Finite-time consensus of high-order heterogeneous multi-agent systems with mismatched disturbances and nonlinear dynamics[J].Nonlinear Dynamics，2019，96（2）：1317-1333.
[12] POLYAKOV A.Nonlinear feedback design for fixed-time stabilization of linear control systems[J].IEEE Transactions on Automatic Control，2011，57（8）：2106-2110.
[13] NING B D，ZUO Z Y，JIN J，et al.Distributed fixed-time coordinated tracking for nonlinear multi-agent systems under directed graphs[J].Asian Journal of Control，2018，20（2）：646-658.
[14] WANG H，YU W W，WEN G H，et al.Fixed-time consensus of nonlinear multi-agent systems with general directed topologies[J].IEEE Transactions on Circuits and Systems II：Express Briefs，2018，66（9）：1587-1591.
[15] WANG H，YU W W，WEN G H，et al.Finite-time bipartite consensus for multi-agent systems on directed signed networks[J].IEEE Transactions on Circuits and Systems I：Regular Papers，2018，65（12）：4336-4348.
[16] LIU J，YU Y，WANG Q，et al.Fixed-time event-triggered consensus control for multi-agent systems with nonlinear uncertainties[J].Neurocomputing，2017，260：497-504.
[17] LIU J，YU Y，SUN J，et al.Distributed event-triggered fixed-time consensus for leader-follower multiagent systems with nonlinear dynamics and uncertain disturbances[J].International Journal of Robust and Nonlinear Control，2018，28（11）：3543-3559.
[18] 陈世明，邵赛.基于事件触发非线性多智能体系统的固定时间一致性[J].控制理论与应用，2019，36（10）：1606-1614.
CHEN S M，SHAO S.Distributed event-triggered fixed-time consensus control for multi-agent systems with nonlinear uncertainties[J].Control Theory & Applications，2019，36（10）：1606-1614.
[19] 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.
[20] GODSIL C，ROYLE G.Algebraic graph theory[M].New York：Springer-Verlag，2001：1-3.
[21] ALTAFINI C.Consensus problems on networks with antagonistic interactions[J].IEEE Transactions on Automatic Control，2012，58（4）：935-946.
[22] GOLDBERG M.Equivalence constants for Ip norms of matrices[J].Linear & Multilinear Algebra，1987，21（2）：173-179.
[23] TABUADA P.Event-triggered real-time scheduling of stabilizing control tasks[J].IEEE Transactions on Automatic Control，2007，52（9）：1680-1685.