Leader-Follower Density Control of Spatial Dynamics in Large-Scale Multi-Agent Systems

TL;DR

This paper develops control strategies for managing the density of large multi-agent systems by manipulating leader agents, ensuring stability and adaptability in multi-dimensional environments through novel feedback architectures.

Contribution

It introduces two new control architectures for density regulation in multi-agent systems, extending previous one-dimensional methods to multi-dimensional scenarios with proven stability.

Findings

Feasibility conditions for density control established.

Two control architectures demonstrated to ensure global stability.

Validated through numerical simulations for various group sizes.

Abstract

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 feed-forward 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 one-dimensional setting, are extended to multi-dimensional cases, and validated through numerical simulations for representative control applications, both for groups of infinite and finite size.