Network structure identification via Koopman analysis and sparse identification

Abstract

This paper considers the identification problem of network structures for networked dynamical systems. We define the network structure as a coupling function describing the network connectivity and the nonlinear data exchange functions in the network, and attempt to identify the coupling function from potentially noisy measurement data. We develop an identification method of network structures applicable even to network systems consisting of nonlinear systems and nonlinear coupling functions by using the Koopman operator theory. First, we design observable functions as basis functions of a functional space, and determine the Koopman operators associated with the dynamics of the network. Then, the coupling function is identified as a projection on the span of the observables. Also, we make use of the sparse identification techniques to reduce requirements on data amounts and improve robustness with respect to measurement noise. Numerical examples show that the proposed method is applicable to a wide range of nonlinear systems, including chaotic systems with nonlinear coupling functions, and yields better performance than some existing methods. Identification results for two different nonlinear network systems with nonlinear coupling functions show the usefulness of the proposed method.