Leader-based multi-agent coordination: controllability and optimal control

In this paper, we consider the situation where a collection of leaders dictate the motion of the followers in heterogenous multi-agent applications. In particular, the followers move according to a decentralized averaging rule, while the leaders' motion is unconstrained. Thus, the trajectories of the leaders can be viewed as exogenous control inputs, which allows us to state and study questions concerning controllability and optimal control.