Distributed Network Design for Laplacian Eigenvalue Placement
Distributed Network Design for Laplacian Eigenvalue Placement
复制标题
拉普拉斯特征值放置的分布式网络设计
DOI：
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复制
发表时间：
2017
影响因子：
4.2
通讯作者：
M. Zavlanos
中科院分区：
文献类型：
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作者：
V. Preciado;M. Zavlanos
我们提出了一种分布式迭代算法，其中一组内联公式notation=“LaTeX”>；$n$<；/tex-math>；<；/inline-formula>；自治代理自组织其通信网络的结构，以控制网络的拉普拉斯特征值谱。我们假设每个代理只能访问其周围网络的本地(“短视”)视图，并且没有集中式协调器。在我们的算法的每一次迭代中，代理共享关于他们的网络近视视图的信息，以便分布式地找到最有益的全局边添加/删除，定义为最小化在拉普拉斯谱空间中定义的伪度量。所提出的伪距是根据拉普拉斯谱矩定义的，并且允许高效的分布式实现。该方法本质上是贪婪的，通过构造是稳定的，即局部最小化网络的特征值谱到期望谱的距离。我们用几个数值模拟来说明我们的方法的性能。
We propose a distributed iterative algorithm in which a group of <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> autonomous agents self-organize the structure of their communication network in order to control the network's Laplacian eigenvalue spectrum. We assume that every agent has only access to a local (“myopic”) view of the network around it and that there is no centralized coordinator. With every iteration of our algorithm, the agents share <italic>local</italic> information about their myopic views of the network in order to distributedly find the most beneficial <italic>global</italic> edge addition/deletion, defined as the one that minimizes a pseudometric defined in the space of Laplacian spectra. The proposed pseudometric is defined in terms of the Laplacian spectral moments and allows for an efficient distributed implementation. The proposed approach is greedy in nature and stable by construction, that is, it locally minimizes the distance of the network's eigenvalue spectrum to a desired spectrum. We illustrate the performance of our approach with several numerical simulations.