Topology Inference for Network Systems with Unknown Inputs

TL;DR

This paper introduces a novel two-stage method for inferring the directed topology of network systems from noisy data influenced by unknown, time-varying inputs, combining input detection, filtering, and optimization.

Contribution

It proposes a new two-stage inference scheme that effectively handles unknown inputs and accurately recovers network topology from noisy observations.

Findings

The method accurately detects input injection times with probabilistic guarantees.

The recursive filtering and optimization approach successfully infers the network topology.

Simulations confirm the effectiveness of the proposed topology inference scheme.

Abstract

Topology inference is a powerful tool to better understand the behaviours of network systems (NSs). Different from most of prior works, this paper is dedicated to inferring the directed topology of NSs from noisy observations, where the nodes are influenced by unknown time-varying inputs. These inputs can be actively injected signals by the user, intrinsic system noises or extrinsic environment interference. To tackle this challenging problem, we propose a two-stage inference scheme to overcome the influence of the inputs. First, by leveraging the second-order difference of the state evolution, we establish a judging criterion to detect the input injection time and provide the probability guarantees. With this injection time to determine available observations, an initial topology is accordingly inferred to further facilitate the input estimation. Second, utilizing the stability characteristic of the system response, a recursive input filtering algorithm is designed to approximate the zero-input response, which directly reflects the topology structure. Then, we construct a decreasing-weight based optimization problem to infer the final network topology from the approximated response. Comprehensive simulations demonstrate the effectiveness of the proposed method.