论文标题
通过环固化输入激发的未知网络线性动力学系统的拓扑学习
Topology Learning of unknown Networked Linear Dynamical System excited by Cyclostationary inputs
论文作者
论文摘要
网络动力学系统的拓扑学习是一个重要的问题，对最佳控制，网络的决策，网络安全和安全性有影响。一致拓扑估计的大多数先前工作依赖于时间不相关的过程激发的动态系统。在本文中，我们提出了一种新的算法，用于确保网络的拓扑学习，这些学习是通过时间（彩色）环固化过程激发的，该过程涵盖了包括广义平稳的各种时间相关性。此外，与先前的工作不同，该框架适用于具有复杂有价值依赖关系的线性动态系统，并利用组套索正规化以有效学习网络结构。在本文的第二部分中，当网络的子集未观察到时，我们分析了双向树网络的一致拓扑学习条件。在这里，仅从观察到的节点的时间序列中恢复了完整的拓扑以及未观察到的节点。我们的理论贡献在模拟数据以及现实世界的气候数据上得到了验证。
Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on dynamical systems excited by temporally uncorrelated processes. In this article, we present a novel algorithm for guaranteed topology learning of networks that are excited by temporally (colored) cyclostationary processes, which encompasses a wide range of temporal correlation including wide-sense stationarity. Furthermore, unlike prior work, the framework applies to linear dynamic system with complex valued dependencies, and leverages group lasso regularization for effective learning of the network structure. In the second part of the article, we analyze conditions for consistent topology learning for bidirected tree networks when a subset of the network is unobserved. Here, the full topology along with unobserved nodes are recovered from observed node's time-series alone. Our theoretical contributions are validated on simulated data as well as on real-world climate data.
