Leader–Follower Density Control of Spatial Dynamics in Large-Scale Multiagent Systems

We address the problem of controlling the density of a large ensemble of follower agents by acting on a group of leader agents that interact with them. Using coupled partial integro-differential equations to describe leader and follower density dynamics, we establish feasibility conditions and develop two control architectures ensuring global stability. The first employs feedforward control on the followers' and a feedback on the leaders' density. The second implements a dual feedback loop through a reference-governor that adapts the leaders' density based on both populations' measurements. Our methods, initially developed in a 1-D setting, are extended to higher dimensions and validated through numerical simulations on representative control applications, both for groups of infinite and finite size.