Learning the Exact Topology of Undirected Consensus Networks
This provides a method for non-invasively reconstructing network structures in consensus systems, which is incremental but addresses a specific bottleneck in topology learning.
The paper tackles the problem of learning the exact interaction topology of undirected consensus networks from time series data, and shows that spurious edges from Wiener filtering can be identified using frequency response, enabling exact reconstruction as demonstrated through simulations and experiments on a five-node Raspberry Pi network.
In this article, we present a method to learn the interaction topology of a network of agents undergoing linear consensus updates in a non invasive manner. Our approach is based on multivariate Wiener filtering, which is known to recover spurious edges apart from the true edges in the topology. The main contribution of this work is to show that in the case of undirected consensus networks, all spurious links obtained using Wiener filtering can be identified using frequency response of the Wiener filters. Thus, the exact interaction topology of the agents is unveiled. The method presented requires time series measurements of the state of the agents and does not require any knowledge of link weights. To the best of our knowledge this is the first approach that provably reconstructs the structure of undirected consensus networks with correlated noise. We illustrate the effectiveness of the method developed through numerical simulations as well as experiments on a five node network of Raspberry Pis.