Information centrality and optimal leader selection in noisy networks

Katherine Fitch, Naomi Ehrich Leonard

Research output: Chapter in Book/Report/Conference proceedingConference contribution

44 Scopus citations

Abstract

We consider the leader selection problem in which a system of networked agents, subject to stochastic disturbances, uses a decentralized coordinated feedback law to track an unknown external signal, and only a limited number of agents, known as leaders, can measure the signal directly. The optimal leader selection minimizes the total system error by minimizing the steady-state variance about the external signal, equivalent to an H2 norm of the linear stochastic network dynamics. Efficient greedy algorithms have been proposed in the literature for similar optimal leader selection problems. In contrast, we seek systematic solutions. We prove that the single optimal leader is the node in the network graph with maximal information centrality. In the case of two leaders, we prove that the optimal pair maximizes a joint centrality, which depends on the information centrality of each leader and how well the pair covers the graph. We apply these results to solve explicitly for the optimal single leader and the optimal pair of leaders in special classes of network graphs. To generalize we compute joint centrality for m leaders.

Original languageEnglish (US)
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7510-7515
Number of pages6
ISBN (Print)9781467357173
DOIs
StatePublished - Jan 1 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other52nd IEEE Conference on Decision and Control, CDC 2013
CountryItaly
CityFlorence
Period12/10/1312/13/13

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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    Fitch, K., & Leonard, N. E. (2013). Information centrality and optimal leader selection in noisy networks. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 7510-7515). [6761082] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6761082