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dc.contributor.authorSarkar, Tuhin
dc.contributor.authorRoozbehani, Mardavij
dc.contributor.authorDahleh, Munther A
dc.date.accessioned2020-03-30T14:30:51Z
dc.date.available2020-03-30T14:30:51Z
dc.date.issued2018-10
dc.identifier.issn2325-5870
dc.identifier.issn2372-2533
dc.identifier.urihttps://hdl.handle.net/1721.1/124407
dc.description.abstractThis paper examines the dependence of network performance measures on network size and considers scaling results for large networks. We connect two performance measures that are well studied, but appear to be unrelated. The first measure is concerned with energy metrics, namely the <formula><tex>$H2$</tex></formula>-norm of a network, which arises in control theory applications. The second measure is concerned with the notion of &#x201C;tail risk&#x201D; which arises in economic and financial networks. We study the question of why such performance measures may deteriorate at a faster rate than the growth rate of the network. We first focus on the energy metric and its well known connection to controllability Gramian of the underlying dynamical system. We show that undirected networks exhibit the most graceful energy growth rates as network size grows. This rate is quantified completely by the proximity of spectral radius to unity or distance to instability. In contrast, we show that the simple characterization of energy in terms of network spectrum does not exist for directed networks. We demonstrate that, for any fixed distance to instability, energy of a directed network can grow at an exponentially faster rate. We provide general methods for manipulating networks to reduce energy. In particular, we prove that certain operations that increase the symmetry in a network cannot increase energy (in an order sense). Additionally, we demonstrate that such operations can effectively reduce energy for many network topologies. Secondly, we focus on tail risk in economic and financial networks. In contrast to H2-norm which arises from computing the expectation of energy in the network, tail risk focuses on tail probability behavior of network variables. Although the two measures differ substantially we show that they are precisely connected through the system Gramian. This surprising result explains why topology considerations rather than specific performance measures dictate the large scale behavior of networks. Finally, we demonstrate the consistency of our theory with simulations on synthetic and real life networks. Keywords: Network topology; Topology; Control systems; Robustness; Economics; Symmetric matrices; Electric shocken_US
dc.language.isoen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1109/tcns.2018.2878504en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleAsymptotic Network Robustnessen_US
dc.typeArticleen_US
dc.identifier.citationSarkar, Tuhin, Roozbehani, Mardavij and Dahleh, Munther A. "Asymptotic Network Robustness." IEEE Transactions on Control of Network Systems 6, 2 (June 2019): 812 - 821 ©2018 IEEE.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Institute for Data, Systems, and Societyen_US
dc.contributor.departmentMassachusetts Institute of Technology. Laboratory for Information and Decision Systemsen_US
dc.relation.journalIEEE Transactions on Control of Network Systemsen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2019-05-14T17:08:17Z
dspace.date.submission2019-05-14T17:08:18Z
mit.journal.volume6en_US
mit.journal.issue2en_US


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