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Information centrality and optimal leader selection in noisy networks

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Katherine Fitch and Naomi Ehich Leonard

*Proceedings of the IEEE Conference on Decision and Control*, Florence, Italy,
2013.

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 *H*_{2} 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.

(198 KB pdf)
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