Path-based data-informativity conditions for single module identification in dynamic networks

For consistent or minimum variance estimation of a single module in a dynamic network, a predictor model has to be chosen with selected inputs and outputs, composed of a selection of measured node signals and possibly external excitation signals. The predictor model has to be chosen in such a way that consistent estimation of the target module is possible, under the condition that we have data-informativity for the considered predictor model set. Consistent and minimum variance estimation of target modules is typically obtained if we follow a direct method of identification and predictor model selection, characterized by the property that measured node signals are the prime predictor input signals. In this paper the concept of data-informativity for network models will be formalized, and for the direct method the required data-informativity conditions will be specified in terms of path-based conditions on the graph of the network model, guaranteeing data-informativity in a generic sense, i.e. independent on numerical values of the network transfer functions concerned.