  We study the problem of leader selection in leader-follower multi-agent
systems that are subject to stochastic disturbances. This problem arises in
applications such as vehicle formation control, distributed clock
synchronization, and distributed localization in sensor networks. We pose a new
leader selection problem called the in-network leader selection problem.
Initially, an arbitrary node is selected to be a leader, and in all consequent
steps the network must have exactly one leader. The agents must collaborate to
find the leader that minimizes the variance of the deviation from the desired
trajectory, and they must do so within the network using only communication
between neighbors. To develop a solution for this problem, we first show a
connection between the leader selection problem and a class of discrete
facility location problems. We then leverage a previously proposed
self-stabilizing facility location algorithm to develop a self-stabilizing
in-network leader selection algorithm for acyclic graphs.
