Spectral identification of networks with inputs
For researchers studying network dynamics, this incremental extension removes the need for multiple independent trajectories in autonomous systems, but remains limited to linear dynamics.
This paper extends spectral network identification to networks with external inputs, enabling recovery of Laplacian eigenvalues from limited measurements. The method estimates node degree bounds and aids network clustering, demonstrated on examples.
We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These eigenvalues allow to deduce some global properties of the network, such as bounds on the node degree. Having recently introduced this approach for autonomous networks of nonlinear systems, we extend it here to treat networked systems with external inputs on the nodes, in the case of linear dynamics. This is more natural in several applications, and removes the need to sometimes use several independent trajectories. We illustrate our framework with several examples, where we estimate the mean, minimum, and maximum node degree in the network. Inferring some information on the leading Laplacian eigenvectors, we also use our framework in the context of network clustering.