A frequency approach to topological identification and graphical modeling

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.