Optimal Selection of Observations for Identification of Multiple Modules in Dynamic Networks

This article presents a systematic algorithm to select a set of auxiliary measurements in order to consistently identify certain transfer functions in a dynamic network from observational data. The selection of the auxiliary measurements is obtained by minimizing an appropriate cost function. It is assumed that the topology of the network is known, the forcing inputs are not measured, and the observations have positive additive costs. It is shown that sufficient and necessary conditions for consistent identification of a single transfer function based on a multi-input single-output prediction error method, are equivalent to the notion of minimum cut in an augmented graph resulted from systematically manipulating the graphical representation of the network. Then, the optimal set of auxiliary measurements minimizing the cost could be found using different approaches such as algorithms from graph theory (i.e., Ford-Fulkerson), distributed algorithms (i.e., push-relabel algorithm), or purely optimization based procedures (i.e., linear programming). The results are also extended to the more challenging scenario, where the objective is simultaneously identifying multiple transfer functions.