Optimal Control of a Collective Migration Model

TL;DR

This paper models collective animal migration using a social dynamics system and derives optimal control strategies that designate certain agents as leaders or followers to achieve group consensus efficiently.

Contribution

It introduces a novel optimal control framework for collective migration, identifying strategies that control the most divergent agents as leaders to reach target velocity.

Findings

Optimal control involves controlling agents furthest from the target velocity.

Controlled agents act as leaders, uncontrolled as followers.

Existence of an 'Inactivation' period before full control is optimal.

Abstract

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.