Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems
Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems
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DOI：
10.1016/j.automatica.2010.03.006
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Wenwu Yu;Guanrong Chen;M. Cao
中科院分区：
文献类型：
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作者：
Wenwu Yu;Guanrong Chen;M. Cao
研究了多智能体动态系统二阶一致性的充分必要条件。首先，对每个agent的二阶动力学由位置项和速度项控制，且渐近速度为常数的情况进行了基本的理论分析。给出了保证二阶一致性的充分必要条件，并发现相应网络的拉普拉斯矩阵特征值的实部和虚部在一致性中起着关键作用。在此基础上，导出了面向通信延迟的多智能体系统的二阶一致性算法。给出了网络拓扑包含有向生成树的多智能体系统当且仅当时延小于一个临界值时，能够达成一致的充要条件。最后通过仿真算例验证了理论分析的正确性。
This paper studies some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. First, basic theoretical analysis is carried out for the case where for each agent the second-order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant. A necessary and sufficient condition is given to ensure second-order consensus and it is found that both the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network play key roles in reaching consensus. Based on this result, a second-order consensus algorithm is derived for the multi-agent system facing communication delays. A necessary and sufficient condition is provided, which shows that consensus can be achieved in a multi-agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value. Finally, simulation examples are given to verify the theoretical analysis.