  Collective migration of animals in a cohesive group is rendered possible by a
strategic distribution of tasks among members: some track the travel route,
which is time and energy-consuming, while the others follow the group by
interacting among themselves. In this paper, we study a social dynamics system
modeling collective migration. We consider a group of agents able to align
their velocities to a global target velocity, or to follow the group via
interaction with the other agents. The balance between these two attractive
forces is our control for each agent, as we aim to drive the group to consensus
at the target velocity. We show that the optimal control strategies in the case
of final and integral costs consist of controlling the agents whose velocities
are the furthest from the target one: these agents sense only the target
velocity and become leaders, while the uncontrolled ones sense only the group,
and become followers. Moreover, in the case of final cost, we prove an
"Inactivation" principle: there exist initial conditions such that the optimal
control strategy consists of letting the system evolve freely for an initial
period of time, before acting with full control on the agent furthest from the
target velocity.
