Edge Agreement: Graph-Theoretic Performance Bounds and Passivity Analysis
Edge Agreement: Graph-Theoretic Performance Bounds and Passivity Analysis
复制标题
DOI：
10.1109/tac.2010.2056730
复制
发表时间：
2011-03
影响因子：
6.8
通讯作者：
Daniel Zelazo;M. Mesbahi
中科院分区：
文献类型：
--
作者：
Daniel Zelazo;M. Mesbahi
这项工作探讨了在边缘一致性问题的背景下图拉普拉斯算子的边缘变体的属性。我们表明，边缘拉普拉斯算子及其相应的协议协议为众所周知的节点协议或共识算法提供了有用的视角。具体来说，边缘拉普拉斯算子引起的动力学有助于更好地理解某些子图（例如循环和生成树）在原始一致性问题中的作用。使用边缘拉普拉斯算子，我们继续检查协议协议的 H2 和 H∞ 性能的图论特征。这些结果随后应用于基于共识的应用程序的最佳传感器放置环境中。最后，边缘拉普拉斯算子被用来为具有被动动力学的代理的线性协议的非线性扩展提供新的见解。
This work explores the properties of the edge variant of the graph Laplacian in the context of the edge agreement problem. We show that the edge Laplacian, and its corresponding agreement protocol, provides a useful perspective on the well-known node agreement, or the consensus algorithm. Specifically, the dynamics induced by the edge Laplacian facilitates a better understanding of the role of certain subgraphs, e.g., cycles and spanning trees, in the original agreement problem. Using the edge Laplacian, we proceed to examine graph-theoretic characterizations of the H2 and H∞ performance for the agreement protocol. These results are subsequently applied in the contexts of optimal sensor placement for consensus-based applications. Finally, the edge Laplacian is employed to provide new insights into the nonlinear extension of linear agreement to agents with passive dynamics.