Allocation of Excitation Signals for Generic Identifiability of Dynamic Networks

This paper studies generic identifiability of dynamic networks, in which the edges connecting the vertex signals are described by proper transfer functions, and partial vertices are excited by designed external signals. We assume that the topology of the underlying graph is known, and all the vertex signals are measured. We show that generic identifiability of a directed network is related to the existence of a set of disjoint directed pseudo-trees that cover all the edges of the underlying graph, based on which, an excitation allocation problem is studied, aiming to select the minimal number excitation signals to achieve the generic identifiability of the whole network. An algorithmic procedure thereby is devised for selecting locations of the external signals such that all the edges can be consistently estimated.