In this article, we explore the state-space formulation of a network process to recover from partial observations the network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology identification problem. This approach provides a unified view of network control and signal processing on graphs. In addition, we provide theoretical guarantees for the recovery of the topological structure of a deterministic continuous-time linear dynamical system from input-output observations even when the input and state interaction networks are different. Our mathematical analysis is accompanied by an algorithm for identifying from data,a network topology consistent with the system dynamics and conforms to the prior information about the underlying structure. The proposed algorithm relies on alternating projections and is provably convergent. Numerical results corroborate the theoretical findings and the applicability of the proposed algorithm.

中文翻译：

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基于局部观测的状态空间网络拓扑识别

在本文中，我们探索了网络过程的状态空间公式，以从部分观察中恢复驱动其动态性的网络拓扑。为此，我们采用从系统识别文献中借用的子空间技术，并将其扩展到网络拓扑识别问题。这种方法在图形上提供了网络控制和信号处理的统一视图。此外，即使输入和状态交互网络不同，我们也能为从输入输出观察中恢复确定性连续时间线性动力系统的拓扑结构提供理论保证。我们的数学分析伴随着一种算法，该算法可从数据中识别出与系统动力学一致的网络拓扑，并符合有关底层结构的先验信息。所提出的算法依赖于交替投影并且证明是收敛的。数值结果证实了该算法的理论发现和适用性。