线性多智能体系统的自适应动态事件触发一致性
Adaptive Dynamic Event-Triggered Consensus of Linear Multi-Agent Systems
摘要: 本文研究了一般线性多智能体系统的自适应动态事件触发一致性问题。通过提出一种分布式自适应事件触发控制协议，有效避免了对网络拓扑全局信息的依赖，降低了通信频率。在给出的事件触发条件中，为每个智能体引入一个辅助函数来动态调节其阈值。与传统的静态阈值相比，动态阈值能够保证更少的事件触发时刻。首先，通过模型变换，将多智能体系统的一致性问题转化为相应误差系统的稳定性问题。进一步，利用代数图论和Lyapunov稳定性理论，得到了多智能体系统达到一致的充分性判据。同时，证明了在所提出的事件触发条件下，能够有效地排除Zeno行为。最后，通过仿真实例验证了理论结果的有效性。
Abstract: This paper is concerned with adaptive dynamic event-triggered consensus of general linear multi-agent systems. The dependence on the global information of network topology can be avoided and the communication frequency can be reduced by proposing a distributed adaptive event-triggered control protocol. In the event-triggered condition, an auxiliary function is intro-duced for each agent to regulate its threshold dynamically. Compared with the traditional static threshold, the dynamic one can ensure less event-triggered instants. First, by model transformation, the consensus problem of multi-agent systems is transformed into the stability problem of the corresponding error systems. Furthermore, by using algebraic graph theory and Lyapunov stability theory, some sufficient criteria for multi-agent systems to achieve consensus are obtained. Meanwhile, it is proved that the proposed event-triggered conditions can exclude Zeno behavior effectively. One simulation example is provided to validate the effectiveness of obtained theoretical results.
文章引用：田昌源, 刘开恩, 崔丹丹. 线性多智能体系统的自适应动态事件触发一致性[J]. 理论数学, 2021, 11(11): 1770-1780. https://doi.org/10.12677/PM.2021.1111200

参考文献

[1] Savkin, A.V., Wang, C., Baranzadeh, A., Xi, Z.Y. and Nguyen, H. (2016) Distributed Formation Building Algorithms for Groups of Wheeled Mobile Robots. Robotics and Autonomous Systems, 75, 463-474. [Google Scholar] [CrossRef] 
[2] Ji, Z.J., Lin, H., Cao, S.B., Qi, Q.Y. and Ma, H. (2021) The Complexity in Complete Graphic Characterizations of Multi-Agent Controllability. IEEE Transactions on Cybernetics, 51, 64-76. [Google Scholar] [CrossRef] 
[3] Wang, D.D., Zhou, Q.H. and Zhu, W. (2018) Adaptive Event-Based Consensus of Multi-Agent Systems with General Linear Dynamics. Journal of Systems Science & Com-plexity, 31, 120-129. [Google Scholar] [CrossRef] 
[4] 叶丹, 张天予, 李奎. 全局信息未知的多智能体自适应容错包容控制[J]. 山东大学学报(工学版), 2017, 47(5): 1-6.
[5] Cheng, L., Wang, Y.P., Hou, Z.G., Tan, M. and Cao, Z.Q. (2013) Sampled-Data Based Average Consensus of Second-Order Integral Multi-Agent Systems: Switching Topologies and Communication Noises. Automatica, 49, 1458-1464. [Google Scholar] [CrossRef] 
[6] Dimrogonas, D.V., Frazzoli, E. and Johansson, K.H. (2012) Distributed Event-Triggered Control for Multi-Agent Systems. IEEE Transactions on Automatic Control, 57, 1291-1297. [Google Scholar] [CrossRef] 
[7] Fan, Y., Feng, G., Wang, Y. and Song C. (2013) Distributed Event-Triggered Control of Multi-Agent Systems with Combinational Measurements. Automatica, 49, 671-675. [Google Scholar] [CrossRef] 
[8] Shang, Y.L. (2018) Fixed-Time Group Consensus for Multi-Agent Systems with Non-Linear Dynamics and Uncertainties. IET Control Theory & Applications, 12, 395-404. [Google Scholar] [CrossRef] 
[9] Li, X.D, Peng, D.X. and Cao, J.D. (2020) Lyapunov Stability for Impulsive Systems via Event-Triggered Impulsive Control. IEEE Transactions on Automatic Control, 65, 4908-4913. [Google Scholar] [CrossRef] 
[10] Liu, K.E. and Ji, Z.J. (2017) Consensus of Multi-Agent Systems with Time Delay Based on Periodic Sample and Event Hybrid Control. Neurocomputing, 270, 11-17. [Google Scholar] [CrossRef] 
[11] Liu, K.E., Ji, Z.J. and Zhang, X.F. (2020) Periodic Event-Triggered Consensus of Multi-Agent Systems Under Directed Topology. Neurocomputing, 385, 33-41. [Google Scholar] [CrossRef] 
[12] Ai, X.L. and Wang, L. (2021) Distributed Fixed-Time Event-Triggered Consensus of Linear Multi-Agent Systems with Input Delay. International Journal of Robust and Nonlinear Control, 31, 2526-2545. [Google Scholar] [CrossRef] 
[13] Li, Z.K., Ren, W., Liu, X.D. and Fu, M.Y. (2013) Consensus of Multi-Agent Systems with General Linear and Lipschitz Non-Linear Dynamics Using Distributed Adaptive Protocols. IEEE Transactions on Automatic Control, 58, 1786-1791. [Google Scholar] [CrossRef] 
[14] Yu, Z.Y., Yu, S.Z., Jiang, H.J. and Hu, C. (2021) Distributed Consensus for Multi-Agent Systems via Adaptive Sliding Mode Control. International Journal of Robust and Nonlinear Control, 31, 7125-7151. [Google Scholar] [CrossRef] 
[15] Zhu, W., Zhou, Q.H., Wang, D.D. and Feng, G. (2018) Fully Distributed Consensus of Second-Order Multi-Agent Systems Using Adaptive Event-Based Control. Science China Information Sciences, 61, Article No. 129201. [Google Scholar] [CrossRef] 
[16] Cheng, B. and Li, Z.K. (2019) Fully Distributed Event-Triggered Protocols for Linear Multi-Agent Networks. IEEE Transactions on Automatic Control, 64, 1655-1662. [Google Scholar] [CrossRef] 
[17] Li, X.W., Sun, Z.Y., Tang, Y. and Karimi, H.R. (2021) Adaptive Event-Triggered Consensus of Multi-Agent Systems on Directed Graphs. IEEE Transactions on Automatic Control, 66, 1670-1685. [Google Scholar] [CrossRef] 
[18] Yi, X.L., Liu, K., Dimarogonas, D.V. and Johansson, K.H. (2019) Dynamic Event-Triggered and Self-Triggered Control for Multi-Agent Systems. IEEE Transactions on Automatic Control, 64, 3300-3307. [Google Scholar] [CrossRef] 
[19] Du, S.L., Liu, T. and Ho, D.W.C. (2020) Dynamic Event-Triggered Control for Leader-Following Consensus of Multi-Agent Systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50, 3243-3251. [Google Scholar] [CrossRef] 
[20] Li, Y.F., Liu, X.D., Liu, H.K., Du, C.K. and Lu, P.L. (2021) Distributed Dynamic Event-Triggered Consensus Control for Multi-Agent Systems under Fixed and Switching Topol-ogies. Journal of the Franklin Institute, 358, 4348-4372. [Google Scholar] [CrossRef] 
[21] He, W.L., Xu, B., Han Q.L. and Qian F. (2020) Adaptive Consensus Control of Linear Multi-Agent Systems with Dynamic Event-Triggered Strategies. IEEE Transactions on Cybernetics, 50, 2996-3008. [Google Scholar] [CrossRef] 
[22] Bernstein, D.S. (2009) Matrix Mathematics: Theory, Facts, and Formulas. Princeton University Press, Princeton. [Google Scholar] [CrossRef] 
[23] Li, Z.K. and Duan Z. (2017) Cooperative Control of Multi-Agent Systems: A Consensus Region Approach. CRC Press, Boca Raton. [Google Scholar] [CrossRef] 

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