Learning the Exact Topology of Undirected Consensus Networks

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.Comment: 6 page

Data-driven identification of a thermal network in multi-zone building

System identification of smart buildings is necessary for their optimal control and application in demand response. The thermal response of a building around an operating point can be modeled using a network of interconnected resistors with capacitors at each node/zone called RC network. The development of the RC network involves two phases: obtaining the network topology, and estimating thermal resistances and capacitance's. In this article, we present a provable method to reconstruct the interaction topology of thermal zones of a building solely from temperature measurements. We demonstrate that our learning algorithm accurately reconstructs the interaction topology for a $5$ zone office building in EnergyPlus with real-world conditions. We show that our learning algorithm is able to recover the network structure in scenarios where prior research prove insufficient.Comment: 6 pages, 12 figures, 57th IEEE Conference on Decision and Contro

Physics Informed Topology Learning in Networks of Linear Dynamical Systems

Learning influence pathways of a network of dynamically related processes from observations is of considerable importance in many disciplines. In this article, influence networks of agents which interact dynamically via linear dependencies are considered. An algorithm for the reconstruction of the topology of interaction based on multivariate Wiener filtering is analyzed. It is shown that for a vast and important class of interactions, that respect flow conservation, the topology of the interactions can be exactly recovered. The class of problems where reconstruction is guaranteed to be exact includes power distribution networks, dynamic thermal networks and consensus networks. The efficacy of the approach is illustrated through simulation and experiments on consensus networks, IEEE power distribution networks and thermal dynamics of buildings.Comment: 14 pages, 10 figure

Topology Learning of Linear Dynamical Systems with Latent Nodes using Matrix Decomposition

In this article, we present a novel approach to reconstruct the topology of linear dynamical systems with latent nodes. The network is allowed to have directed loops and bi-directed edges. We show that the imaginary part of the inverse power spectral density matrix (IPSDM), realized from the time-series data and shown to be skew symmetric, can unveil the connectivity structure. Necessary and sufficient conditions are provided for the unique decomposition of a given skew symmetric into sum of a sparse skew symmetric and a low rank skew symmetric matrices. An optimization based algorithm is developed to decompose the imaginary part of IPSDM to yield the sparse matrix $\mathbf{S}$ and the low-rank matrix $\mathbf{L}$. $\mathbf{S}$ embeds information about the topology of a subgraph restricted to the observed nodes and $\mathbf{L}$ provides information about the topology between the observed nodes and the hidden nodes. Algorithms are provided to reconstruct the topology of the network between the observed nodes using $\mathbf{S}$ and the links related to latent nodes using $\mathbf{L}$. Moreover, for finite number of data samples, we provide concentration bounds on the entry-wise distance between the true IPSDM and the estimated IPSDM.Comment: 19 pages, 5 figure