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.

This paper considers the identification problem of network structures of interconnected dynamical systems using measured output data. In particular, we propose an identification method based on the measured output data of each node in the network whose dynamic is unknown. The proposed identification method consists of three steps: we first consider the outputs of the nodes to be all the states of the dynamics of the nodes, and the unmeasurable hidden states to be dynamical inputs with unknown dynamics. In the second step, we define the dynamical inputs as new variables and identify the dynamics of the network system with measured output data using Koopman operators. Finally, we extract the network structure from the identified dynamics as the information transmitted via the network. We show that the identified coupling functions, which represent the network structures, are actually projections of the dynamical inputs onto the space spanned by some observable functions. Numerical examples illustrate the validity of the obtained results.

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