A frequency approach to topological identification and graphical modeling

TL;DR

This paper introduces a frequency-based method for topological identification and graphical modeling of dynamical networks without prior assumptions or system testing, useful for systems like transportation networks.

Contribution

It develops a novel frequency approach enabling the exact identification of network topology and graphical models in a blind, test-free scenario.

Findings

Topology of polytree linear networks can be exactly identified.

Method extends to building acyclic graphical models like Bayesian Networks.

Applicable to real systems such as transportation networks.

Abstract

This works explores and illustrates recent results developed by the author in field of dynamical network analysis. The considered approach is blind, i.e., no a priori assumptions on the interconnected systems are available. Moreover, the perspective is that of a simple "observer" who can perform no kind of test on the network in order to study the related response, that is no action or forcing input aimed to reveal particular responses of the system can be performed. In such a scenario a frequency based method of investigation is developed to obtain useful insights on the network. The information thus derived can be fruitfully exploited to build acyclic graphical models, which can be seen as extension of Bayesian Networks or Markov Chains. Moreover, it is shown that the topology of polytree linear networks can be exactly identified via the same mathematical tools. In this respect, it is worth observing that important real systems, such as all the transportation networks, fit this class.