Identifiability in dynamic network identification

Dynamic networks are structured interconnections of dynamical systems driven by external excitation and disturbance signals. We develop the notion of network identifiability, a property of a parameterized model set that ensures that module dynamics are uniquely related to the filters that specify the one-step-ahead predictors of all node signals in the network. It can be used to specify which presence of excitation signals will result in a unique representation of the network dynamics in a particular network model parametrization. This uniqueness is necessary for detecting the topology of the network from measured data, and for consistently estimating the network dynamics. We combine aspects of the classical notion of system identifiability with a uniqueness-oriented parametrization concept, and extend this to the situation of highly structured model sets. All node signals in the network are treated in a symmetric way. The presented concept and theory allow for the incorporation of particular structural prior knowledge of the network structure