Controllability of Bandlimited Graph Processes Over Random Time Varying Graphs
Controllability of Bandlimited Graph Processes Over Random Time Varying Graphs
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DOI：
10.1109/tsp.2019.2952053
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发表时间：
2019-04
影响因子：
5.4
通讯作者：
Fernando Gama;E. Isufi;Alejandro Ribeiro;G. Leus
中科院分区：
文献类型：
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作者：
Fernando Gama;E. Isufi;Alejandro Ribeiro;G. Leus
复杂网络的可控性出现在涉及社会、金融、道路、通信和智能电网的许多技术问题中。在许多实际情况下，底层拓扑可能会随时间随机变化，这是由于链路故障，如改变友谊、路障或传感器故障。因此，如果没有适当地考虑随机性，就会导致控制不佳的动力学。我们考虑了当网络拓扑随时间随机变化时的网络状态控制问题。我们的问题涉及在图上受带宽限制的目标状态；这些状态仅在特定的图频带上具有非零频率内容。因此，我们利用图形信号处理并利用带宽受限模型来从一组固定的控制节点驱动网络状态。当从几个节点控制状态时，我们观察到创建了虚假的带外频率内容。因此，我们专注于在期望的频段内控制网络状态，然后使用图滤波来去除不需要的频率内容。为了考虑拓扑的随机性，我们提出了平均可控性的概念，即将期望的网络状态驱动到目标状态。进行详细的均方误差分析，以量化特定图形实现上的最终控制状态与实际目标状态之间的统计偏差。最后，我们提出了不同的控制策略，并在合成网络模型和社会网络上对它们的有效性进行了评估。
Controllability of complex networks arises in many technological problems involving social, financial, road, communication, and smart grid networks. In many practical situations, the underlying topology might change randomly with time, due to link failures such as changing friendships, road blocks or sensor malfunctions. Thus, it leads to poorly controlled dynamics if randomness is not properly accounted for. We consider the problem of controlling the network state when the topology varies randomly with time. Our problem concerns target states that are bandlimited over the graph; these are states that have nonzero frequency content only on a specific graph frequency band. We thus leverage graph signal processing and exploit the bandlimited model to drive the network state from a fixed set of control nodes. When controlling the state from a few nodes, we observe that spurious, out-of-band frequency content is created. Therefore, we focus on controlling the network state over the desired frequency band, and then use a graph filter to get rid of the unwanted frequency content. To account for the topological randomness, we develop the concept of controllability in the mean, which consists of driving the expected network state towards the target state. A detailed mean squared error analysis is performed to quantify the statistical deviation between the final controlled state on a particular graph realization and the actual target state. Finally, we propose different control strategies and evaluate their effectiveness on synthetic network models and social networks.