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Controllability Gramian spectra of random networks

Preciado, VM and Rahimian, MA (2016) Controllability Gramian spectra of random networks. In: UNSPECIFIED.

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Abstract

We propose a theoretical framework to study the eigenvalue spectra of the controllability Gramian of systems with random state matrices, such as networked systems with a random graph structure. Using random matrix theory, we provide expressions for the moments of the eigenvalue distribution of the controllability Gramian. These moments can then be used to derive useful properties of the eigenvalue distribution of the Gramian (in some cases, even closed-form expressions for the distribution). We illustrate this framework by considering system matrices derived from common random graph and matrix ensembles, such as the Wigner ensemble, the Gaussian Orthogonal Ensemble (GOE), and random regular graphs. Subsequently, we illustrate how the eigenvalue distribution of the Gramian can be used to draw conclusions about the energy required to control random system.


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Details

Item Type: Conference or Workshop Item (UNSPECIFIED)
Status: Published
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Preciado, VM
Rahimian, MARAHIMIAN@pitt.eduRAHIMIAN0000-0001-9384-1041
Date: 28 July 2016
Date Type: Publication
Journal or Publication Title: Proceedings of the American Control Conference
Volume: 2016-J
Page Range: 3874 - 3879
Event Type: Conference
DOI or Unique Handle: 10.1109/acc.2016.7525517
Schools and Programs: Swanson School of Engineering > Industrial Engineering
Refereed: Yes
ISBN: 9781467386821
ISSN: 0743-1619
Date Deposited: 17 Aug 2020 16:55
Last Modified: 19 Oct 2021 05:55
URI: http://d-scholarship.pitt.edu/id/eprint/39616

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