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Emerging Applications of Control and Systems Theory pp 81–92Cite as

Robustness Sensitivities in Large Networks

Part of the Lecture Notes in Control and Information Sciences - Proceedings book series (LNCOINSPRO)

Abstract

This article focuses on developing a framework to assess robustness in large interconnected networks that arise frequently in many socioeconomic networks such as transportation, economics, and opinion dynamics. We first introduce the idea of “asymptotic” resilience, i.e., a measure of robustness to disturbances, as the network size increases, keeping the underlying structure invariant. We argue that such a notion of robustness is different from existing ideas in robust control theory that do not account for network topology and dimension. Under this new framework, we formulate a hierarchy of resilience for different network topologies. We present examples of commonly encountered network topologies and comment on their resilience. We then provide a formal characterization of how edge link perturbation affects resilience in large networks. Further, we show how each node of the network contributes to its resilience and identify critical nodes that become “fragile” as the network dimension grows. A major contribution of our work is that the analysis is no longer limited to undirected networks, as in previous literature.

Keywords

  • Edge Links
  • Large Interconnected Network
  • Nodal Volatilities
  • Standard Control Theory
  • Fragile Link

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    T. Sarkar, M. Roozbehani & M. A. Dahleh

Authors
  1. T. Sarkar
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  2. M. Roozbehani
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  3. M. A. Dahleh
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Corresponding author

Correspondence to T. Sarkar .

Editor information

Editors and Affiliations

  1. IEIIT—CNR, Politecnico di Torino, Turin, Italy

    Prof. Roberto Tempo

  2. Department of Systems Engineering, University of Texas at Dallas, Richardson, Texas, USA

    Prof. Stephen Yurkovich

  3. Russ Engineering Center, Wright State University, Dayton, Ohio, USA

    Pradeep Misra

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Sarkar, T., Roozbehani, M., Dahleh, M.A. (2018). Robustness Sensitivities in Large Networks. In: Tempo, R., Yurkovich, S., Misra, P. (eds) Emerging Applications of Control and Systems Theory. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-67068-3_6

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  • DOI: https://doi.org/10.1007/978-3-319-67068-3_6

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