On the informativity of direct identification experiments in dynamical networks

Data informativity is a crucial property to ensure the consistency of the prediction error estimate. This property has thus been extensively studied in the open-loop and in the closed-loop cases, but has only been briefly touched upon in the dynamic network case. In this paper, we consider the prediction error identification of the modules in a row of a dynamic network using the full input approach. Our main contribution is to propose a number of easily verifiable data informativity conditions for this identification problem. Among these conditions, we distinguish a sufficient data informativity condition that can be verified based on the topology of the network and a necessary and sufficient data informativity condition that can be verified via a rank condition on a matrix of coefficients that are related to a full-order model structure of the network. These data informativity conditions allow to determine different situations (i.e., different excitation patterns) leading to data informativity. In order to be able to distinguish between these different situations, we also propose an optimal experiment design problem that allows to determine the excitation pattern yielding a certain pre-specified accuracy with the least excitation power.