Topological Properties in Identification and Modeling Techniques

Abstract

This contribution deals with the problem of finding models and dependencies within a large set of time series or processes. Nothing is assumed about their mutual influences and connections. The problem can not be tackled efficiently, starting from a classical system identification approach. Indeed, the general optimal solution would provide a large number of models, since it would consider every possible interdependence. Then a suboptimal approach will be developed. The proposed technique will present interesting modeling properties which can be interpreted in terms of graph theory. The application of this procedure will also be exploited as a tool to provide a clusterization of the time series. Finally, we will show that it turns out to be a dynamical generalization of other techniques described in literature.