Modeling and Topology Estimation of Low Rank Dynamical Networks

Center for Systems and Control, School of Advanced Manufacturing and Robotics, and Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing, China (e-mail: amingli@pku.edu.cn).Abstract: Conventional topology learning methods for dynamical networks become inapplicable to processes exhibiting low-rank characteristics. To address this, we propose the low rank dynamical network model which ensures identifiability. By employing causal Wiener filtering, we establish a necessary and sufficient condition that links the sparsity pattern of the filter to conditional Granger causality. Building on this theoretical result, we develop a consistent method for estimating all network edges. Simulation results demonstrate the parsimony of the proposed framework and consistency of the topology estimation approach.