Topology Learning in Radial Dynamical Systems With Unreliable Data

Abstract

Many complex engineering systems admit bidirectional and linear couplings between their agents. Blind and passive methods to identify such influence pathways/couplings from data are central to many applications. However, dynamically related data-streams originating at different sources are prone to corruption caused by asynchronous time-stamps of different streams, packet drops and noise. Such imperfect information may be present in the entire observation period, and hence not detected by change-detection algorithms that require an initial clean observation period. In this article, we provide a novel approach to detect the location of corrupt agents as well as present an algorithm to learn the structure of radial dynamical systems despite corrupted data streams. In particular, we show that our approach provably learns the true radial structure if the unknown corrupted nodes are at least three <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hops</i> away from each other. Our theoretical results are further validated in a test dynamical network.