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arXiv 1709.04153eess.SYcs.SY
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具有输入的网络的谱识别

Spectral identification of networks with inputs

University of Namur(南纳姆大学);Université catholique de Louvain(天主教鲁汶大学)

Alexandre Mauroy, Julien Hendrickx

AI总结:

本文提出了一种用于具有外部输入节点的网络的谱网络识别方法,通过有限信号测量恢复网络拉普拉斯矩阵的特征值,以推断网络的全局属性,如节点度数的界。

摘要:

我们考虑了一组相互连接的动力系统网络。谱网络识别旨在从极少量(可能仅一个)信号的测量中恢复网络拉普拉斯矩阵的特征值。这些特征值允许推断网络的一些全局属性,如节点度数的界。近年来,我们为自主非线性系统网络引入了这种方法,现在将其扩展到具有外部输入节点的网络,情况为线性动力学。这在许多应用中更为自然,并消除了有时需要使用多个独立轨迹的必要。我们通过几个例子说明了我们的框架,其中我们估计网络中节点度数的均值、最小值和最大值。通过推断某些关于主导拉普拉斯特征向量的信息,我们还利用我们的框架在网络聚类的背景下进行应用。

英文摘要:

We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These eigenvalues allow to deduce some global properties of the network, such as bounds on the node degree. Having recently introduced this approach for autonomous networks of nonlinear systems, we extend it here to treat networked systems with external inputs on the nodes, in the case of linear dynamics. This is more natural in several applications, and removes the need to sometimes use several independent trajectories. We illustrate our framework with several examples, where we estimate the mean, minimum, and maximum node degree in the network. Inferring some information on the leading Laplacian eigenvectors, we also use our framework in the context of network clustering.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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