Abstract
We introduce a reachable set based method of leader selection, for achieving minimum time consensus in networks of first order discrete time systems. The systems, also referred as agents, interact over a weighted communication graph, using distributed control protocol proposed by Vicsek in [1]. In addition, a bounded external input is applied to one of the agents, designated a-priory, as the leader. If a time-optimal external input is applied to an agent, the states of the agents are driven from given initial condition to a consensus state in minimum time. The algorithm proposed in this paper identifies the leader such that, for the given initial condition, the minimum time to consensus through the leader, is the least among all possible choices. We show that the state-space of the relative state dynamics can be partitioned using the boundaries of the reachable sets.
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