Optimal excitation and measurement pattern for cascade networks

Abstract

This work deals with the selection of the experimental setting that yields most accurate estimates for a cascade network. There is a number of excitation and measurement patterns in which all modules in a cascade network can be identified. We consider that the optimal experiment is the one that achieves the least trace of the asymptotic covariance matrix of the prediction error method using the minimal number of excitations and measurements combined. We develop theoretical results under the assumptions that all modules are equal and with equal signal-to-noise ratio throughout the network. Under these assumptions, we demonstrate that there is an excitation and measurement pattern that results in more accurate estimates than others. Moreover, we show that some excitation and measurement patterns yield equal overall precision. From these results, guidelines based on the topology of the network emerge for the choice of the experimental setting. We provide numerical results which attest that the principles behind these guidelines are also valid for more general situations.