Identifying Network Structure of Nonlinear Dynamical Systems: Contraction and Kuramoto Oscillators

In this work, we study the identifiability of network topologies for networked nonlinear systems when partial measurements of the nodes are taken. We explore scenarios where different candidate topologies can yield similar measurements, thus limiting identifiability. To do so, we apply the contraction theory framework to facilitate comparisons between candidate topologies. We show that semicontraction in the observable space is a sufficient condition for two systems to become indistinguishable from one another based on partial measurements. We apply this framework to study networks of Kuramoto oscillators, and discuss scenarios in which different topologies (both connected and disconnected) become indistinguishable.