Robust multi-scale leader-follower control of large multi-agent systems

TL;DR

This paper develops a robust control strategy for large multi-agent systems with leader-follower dynamics, ensuring followers reach desired distributions despite uncertainties, by combining continuum modeling and singular perturbation analysis.

Contribution

It introduces a coupled continuum model for leaders and followers under perturbations and designs a macroscopic feedback law with proven convergence guarantees.

Findings

Global asymptotic convergence of followers' density achieved

Explicit leader-to-follower mass ratio bound derived

Numerical simulations validate theoretical results

Abstract

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.