The Observability Radius of Networks
The Observability Radius of Networks
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DOI：
10.1109/tac.2016.2608941
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发表时间：
2016-12
影响因子：
6.8
通讯作者：
G. Bianchin;P. Frasca;A. Gasparri;F. Pasqualetti
中科院分区：
文献类型：
--
作者：
G. Bianchin;P. Frasca;A. Gasparri;F. Pasqualetti
本文研究了网络系统的可观测半径，它衡量了网络对边扰动的鲁棒性。我们考虑线性网络，其中的动态描述的加权邻接矩阵和专用的传感器定位在一个子集的节点。我们允许某些边缘权重的扰动，目的是防止网络动态的某些模式的可观测性。为了符合网络设置，我们的工作考虑了所需的稀疏结构的扰动，从而扩展了经典文献的线性系统的可观测半径。本文提出了两组结果。首先，我们提出了一个优化框架，以确定最小的Frobenius范数，使所需的模式从现有的传感器节点不可观测的扰动。其次，我们研究了具有给定结构和随机边权值的网络的期望可观测半径。我们提供了基本的鲁棒性界限依赖于网络的连通性，我们分析表征线和星星网络的最佳扰动，表明线网络本质上是更强大的比星星网络。
This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix and dedicated sensors are positioned at a subset of nodes. We allow for perturbations of certain edge weights with the objective of preventing observability of some modes of the network dynamics. To comply with the network setting, our work considers perturbations with a desired sparsity structure, thus extending the classic literature on the observability radius of linear systems. The paper proposes two sets of results. First, we propose an optimization framework to determine a perturbation with smallest Frobenius norm that renders a desired mode unobservable from the existing sensor nodes. Second, we study the expected observability radius of networks with given structure and random edge weights. We provide fundamental robustness bounds dependent on the connectivity properties of the network and we analytically characterize optimal perturbations of line and star networks, showing that line networks are inherently more robust than star networks.