Identification in dynamic networks with known interconnection topology

The problem of identifying dynamical models on the basis of measurement data is usually considered in a classical open-loop or closed-loop setting. In this paper this problem is generalized to dynamical systems that operate in a complex interconnection structure and a particular transfer function in the network needs to be identified. It is shown that classical methods of closed-loop identification in the prediction error context, can be generalized to provide consistent model estimates, under specified experimental circumstances. This applies to indirect methods that rely on external excitation signals like two-stage and IV methods, as well as to the direct method that relies on consistent noise models. Graph theoretical tools are presented to verify the topological conditions under which the several methods lead to consistent estimates of the network transfer functions.