Topology Inference for Network Systems: Causality Perspective and Nonasymptotic Performance

• 成果类型: Article
• 署名作者: Li, Yushan; He, Jianping; Chen, Cailian; Guan, Xinping
• 署名单位: Shanghai Jiao Tong University; Shanghai Jiao Tong University; Shanghai Jiao Tong University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3303816
• 发表日期: 2024
• 页码: 3483-3498
• 关键词: topology; Network topology; trajectory; Noise measurement; correlation; mathematical models; Network systems; Causality and correlation modeling; network systems (NSs); nonasymptotic analysis; topology inference

摘要

Topology inference for network systems (NSs) plays a crucial role in many areas. This article advocates a causality-based method based on noisy observations from a single trajectory of an NS, which is represented by the state-space model with general directed topology. Specifically, we first prove its close relationships with the ideal Granger estimator for multiple trajectories and the traditional ordinary least squares (OLS) estimator for a single trajectory. Along with this line, we analyze the nonasymptotic inference performance of the proposed method by taking the OLS estimator as a reference, covering both asymptotically and marginally stable systems. The derived convergence rates and accuracy results suggest the proposed method has better performance in addressing potentially correlated observations and achieves zero inference error asymptotically. Besides, an online/recursive version of our method is established for efficient computation or time-varying cases. Extensions on NSs with nonlinear dynamics are also discussed. Comprehensive tests corroborate the theoretical findings and comparisons with other algorithms highlight the superiority of the proposed method.