Topological Identification in Networks of Dynamical Systems

• Published in: IEEE transactions on automatic control 2010-08, Vol.55 (8), p.1860-1871
• Main Authors: Materassi, D, Innocenti, G
• Format: Article
• Language: English
• Subjects: Applied sciences; Approximation; Arithmetic; Biological system modeling; Complex networks; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Dynamical systems; Exact sciences and technology; Frequency; Graph theory; High frequencies; Inference from stochastic processes; time series analysis; Linear systems; Mathematical analysis; Mathematics; Network topology; Networks; Neural networks; Operational research and scientific management; Operational research. Management science; Portfolio theory; Probability and statistics; Raw materials; Sciences and techniques of general use; Software; Statistics; Stock markets; Time series; Time series analysis; Trees; Unweighted pair group method with arithmetic mean (UPGMA)
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2042347

The paper deals with the problem of reconstructing the tree-like topological structure of a network of linear dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and some useful mathematical properties are derived. Theoretical results to guarantee the correctness of the identification procedure for networked linear systems characterized by a tree topology are provided as well. The paper also suggests the approximation of a complex connected network with a tree in order to detect the most meaningful interconnections. The application of the techniques to the analysis of an actual complex network, i.e., to high frequency time series of the stock market, is extensively illustrated.