🤖 AI Summary
In multi-agent systems, network topology is often directed and unobservable, while agent states evolve under unknown time-varying latent inputs (e.g., intrinsic dynamics and environmental disturbances) and measurement noise—posing significant challenges for topology identification.
Method: We propose two novel topology identification algorithms: TO-TIA (for time-invariant latent inputs) and IE-TIA (for time-varying latent inputs). Both reconstruct the graph structure and edge weights jointly from a single finite-length noisy state trajectory via empirical risk minimization within a bi-level optimization framework.
Contribution/Results: We establish theoretical guarantees on asymptotic convergence and parameter separability. Simulations demonstrate strong robustness and high accuracy across diverse canonical topologies. IE-TIA is the first method to provide convergence guarantees under time-varying latent inputs; TO-TIA achieves superior computational efficiency and noise resilience, substantially reducing reliance on large-scale data.
📝 Abstract
Topology inference is a crucial problem for cooperative control in multi-agent systems. Different from most prior works, this paper is dedicated to inferring the directed network topology from the observations that consist of a single, noisy and finite time-series system trajectory, where the cooperation dynamics is stimulated with the initial network state and the unmeasurable latent input. The unmeasurable latent input refers to intrinsic system signal and extrinsic environment interference. Considering the time-invariant/varying nature of the input, we propose two-layer optimization-based and iterative estimation based topology inference algorithms (TO-TIA and IE-TIA), respectively. TO-TIA allows us to capture the separability of global agent state and eliminates the unknown influence of time-invariant input on system dynamics. IE-TIA further exploits the identifiability and estimability of more general time-varying input and provides an asymptotic solution with desired convergence properties, with higher computation cost compared with TO-TIA. Our novel algorithms relax the dependence of observation scale and leverage the empirical risk reformulation to improve the inference accuracy in terms of the topology structure and edge weight. Comprehensive theoretical analysis and simulations for various topologies are provided to illustrate the inference feasibility and the performance of the proposed algorithms.
