Noninvasive Approximation of Linear Dynamic System Networks Using Polytrees

Firoozeh Sepehr, Donatello Materassi

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of approximating a complex network of linear dynamic systems via a simpler network, with the goal of highlighting the most significant connections. Indeed, paradoxically, an approximate network with fewer edges could be more informative in terms of how a system operates than a more accurate representation including a large number of 'weak' links. Broadly, this article explores the meaning of approximating a network belonging to a certain class using another network belonging to a subset of its class (the set of approximators). We posit that any network approximation algorithm is expected to satisfy at least a congruity property. By congruity, we mean that if the approximated network belongs to the set of approximators, then the algorithm should map it into itself. From a technical perspective, we choose a class of dynamic networks with a directed tree (polytree) structure as a set of approximators and analytically derive a technique, which asymptotically satisfies the congruity property when the observation horizon approaches infinity. Also, we test such a technique using high-frequency financial data. Financial data provide a challenging benchmark since they are not expected to meet the theoretical assumptions behind our methodology, such as linearity or stationarity.

Original languageEnglish (US)
Pages (from-to)1314-1323
Number of pages10
JournalIEEE Transactions on Control of Network Systems
Volume8
Issue number3
DOIs
StatePublished - Jan 1 2021

Bibliographical note

Funding Information:
Manuscript received May 31, 2020; revised June 1, 2020 and December 23, 2020; accepted February 3, 2021. Date of publication March 11, 2021; date of current version September 17, 2021. This work was supported in part by the NSF (CNS CAREER #1553504, and SaTC #1816703). Recommended by Associate Editor M. R. Jovanovic. (Corresponding author: Firoozeh Sepehr.) Firoozeh Sepehr is with the Department of the Electrical Engineering and Computer Science, University of Tennessee Knoxville, Knoxville, TN 37996 USA (e-mail: fsepehr1@vols.utk.edu).

Publisher Copyright:
© 2014 IEEE.

Keywords

  • Linear Dynamic Systems
  • Network Topology
  • Non-invasive Approach
  • Polytree Structure
  • Topology Approximation

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