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Topology Inference for Networked Dynamical Systems: A Causality and Correlation Perspective

Networked dynamical systems (NDSs) have gained considerable attention in recent years, where the networked agents cooperate to accomplish the common task through the interaction topology. In this paper, we focus on the topology inference problem of NDSs. Different from traditional methods, we aim to infer the internal interaction topology from the perspective of node causality and correlation, covering both directed/undirected topology structures and the asymptotic/marginal stabilities of NDSs. Specifically, we propose a causality-based method that takes the noise characteristic into account and asymptotically approaches the real interaction topology structure, with only single round observations over the dynamical process. When the observation number is small, we further design a correlation-based modification to effectively alleviate the influence of noises. We demonstrate the close relation between the proposed method and the traditional Granger estimator and ordinary least square (OLS) estimator in terms of observation rounds and horizon. We further prove the equivalence conditions of the proposed method with the two estimators from the system stability and noise characteristic. The proposed causality-correlation combined method enjoys analogous asymptotic inference performance with Granger estimator of multiple observation rounds, and outperforms OLS estimator in single observation round, verified by extensive simulations.