Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known (or partially known), two associated goals are, to derive estimators for nodes of the network, which cannot be directly observed or are impractical to measure; and to quantitatively identify the dynamic relations between nodes. We address both problems in the challenging scenario where only some outputs of the network are being measured and the inputs are not accessible. The approach makes use of the notion of d-separation for the graph associated with the network. In the considered class of networks, it is shown that the proposed technique can determine or guide the choice of optimal sparse estimators. This article also derives identification methods that are applicable to cases where loops are present providing a different perspective on the problem of closed-loop identification. The notion of d-separation is a central concept in the area of probabilistic graphical models, thus an additional contribution is to create connections between control theory and machine learning techniques.
Bibliographical noteFunding Information:
Manuscript received April 9, 2019; revised September 6, 2019; accepted November 27, 2019. Date of publication December 16, 2019; date of current version September 25, 2020. This work was supported by the National Science Foundation under Grant 1553504 and Grant 1727096, and in part by the NSF CAREER Award 1350504 and ARPA-E AR0000701. Recommended by Associate Editor P. Rapisarda. (Corresponding author: Donatello Materassi.) The authors are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: email@example.com; firstname.lastname@example.org).
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- Graphical models
- stochastic systems
- system identification