Decentralised minimal-time consensus
Decentralised minimal-time consensus
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DOI：
10.1109/cdc.2011.6161213
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
Ye Yuan;G. Stan;Mauricio Barahona;Ling Shi;J. Gonçalves
中科院分区：
文献类型：
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作者：
Ye Yuan;G. Stan;Mauricio Barahona;Ling Shi;J. Gonçalves
本研究考虑了根据最近邻协议交换信息的代理网络的离散时间动态，在该协议下保证所有代理渐近达成共识。我们提出了一种完全去中心化的算法，允许任何代理仅使用其自身历史记录的最小数量的连续值在有限时间内计算整个网络的共识值。我们证明了这个最小步骤数与网络动态的 Jordan 块分解有关，并提出了一种算法，通过检查局部观测的 Hankel 矩阵上的排名条件来获得所讨论的最小步骤数。此外，我们证明最小步骤数与其他代数和图论概念相关，这些概念可以直接从图的拉普拉斯矩阵和底层图拓扑计算。
This study considers the discrete-time dynamics of a network of agents that exchange information according to the nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the consensus value of the whole network in finite time using only the minimal number of successive values of its own history. We show that this minimal number of steps is related to a Jordan block decomposition of the network dynamics and present an algorithm to obtain the minimal number of steps in question by checking a rank condition on a Hankel matrix of the local observations. Furthermore, we prove that the minimal number of steps is related to other algebraic and graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the underlying graph topology.