Consensus problems in networks of agents with switching topology and time-delays
Consensus problems in networks of agents with switching topology and time-delays
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DOI：
10.1109/tac.2004.834113
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发表时间：
2004-09-01
影响因子：
6.8
通讯作者：
Murray, RM
中科院分区：
文献类型：
--
作者：
Olfati-Saber, R;Murray, RM
在本文中，我们讨论了具有固定和切换拓扑的动态代理网络的共识问题。我们分析了三种情况：1）具有固定拓扑的定向网络； 2）带有切换拓扑的网络； 3）没有方向的网络，具有通信时间延迟和固定拓扑。我们介绍了有或没有时间延期的网络的两个共识协议，并在所有三种情况下提供了收敛分析。我们建立了网络的代数连接性（或fiedler特征值）与线性共识协议的性能或谈判速度之间的直接连接。这需要将无方向图的代数连接性概念的概念推广到挖掘物上。事实证明，平衡的挖掘物在解决平均传播问题方面起着关键作用。我们引入了分歧函数，以进行共识协议的收敛分析。分歧函数是分歧网络动力学的Lyapunov函数。我们提出了一个简单的分歧函数，它是一个通用的Lyapunov函数，用于定向网络与开关拓扑的分歧动力学。这项工作的一个独特特征是解决具有定向信息流的网络的共识问题。我们提供依赖代数图理论，矩阵理论和控制理论的分析工具。提供了证明我们理论结果有效性的模拟。
In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.