On Topology Inference for Networked Dynamical Systems: Principles and Performances

Abstract

Topology inference for networked dynamical systems (NDSs) plays a crucial role in many areas. Knowledge of the system topology can aid in detecting anomalies, spotting trends, predicting future behavior and so on. Different from the majority of pioneering works, this paper investigates the principles and performances of topology inference from the perspective of node causality and correlation. Specifically, we advocate a comprehensive analysis framework to unveil the mutual relationship, convergence and accuracy of the proposed methods and other benchmark methods, i.e., the Granger and ordinary least square (OLS) estimators. Our method allows for unknown observation noises, both asymptotic and marginal stabilities for NDSs, while encompasses a correlation-based modification design to alleviate performance degradation in small observation scale. To explicitly demonstrate the inference performance of the estimators, we leverage the concentration measure in Gaussian space, and derive the non-asymptotic rates of the inference errors for linear timeinvariant (LTI) cases. Considering when the observations are not sufficient to support the estimators, we provide an excitationbased method to infer the one-hop and multi-hop neighbors with probability guarantees. Furthermore, we point out the theoretical results can be extended to switching topologies and nonlinear dynamics cases. Extensive simulations highlight the outperformance of the proposed method.

I Can Read Your Mind: Control Mechanism Secrecy of Networked Dynamical Systems under Inference Attacks

“…Theorem 5 (Convergence speed and accuracy of Âo and Âc ; see [80]). Considering the systems (29), with probability at least 1 − δ, the non-asymptotic bound of the OLS estimator Âo satisfies…”