Robust multi-scale leader-follower control of large multi-agent systems
This addresses robust density control for traffic or evacuation scenarios where only some agents are controllable, bridging a gap in existing methods.
The paper tackles the problem of controlling large multi-agent systems with limited actuation by developing a robust multi-scale leader-follower control framework, achieving global asymptotic convergence of followers' density to a desired distribution with an explicit lower bound on the leader-to-follower mass ratio.
In many multi-agent systems of practical interest, such as traffic networks or crowd evacuation, control actions cannot be exerted on all agents. Instead, controllable leaders must indirectly steer uncontrolled followers through local interactions. Existing results address either leader-follower density control of simple, unperturbed multi-agent systems or robust density control of a single directly actuated population, but not their combination. We bridge this gap by deriving a coupled continuum description for leaders and followers subject to unknown bounded perturbations, and designing a macroscopic feedback law that guarantees global asymptotic convergence of the followers' density to a desired distribution. The coupled stability of the leader-follower system is analyzed via singular perturbation theory, and an explicit lower bound on the leader-to-follower mass ratio required for feasibility is derived. Numerical simulations on heterogeneous biased random walkers validate our theoretical findings.