Robust feedback stabilization of interacting multi-agent systems under uncertainty

TL;DR

This paper develops robust control strategies for large-scale multi-agent systems under uncertainty, ensuring stability and bounded variance using $6$ control and mean field models, with numerical validation.

Contribution

It introduces $6$ control design for multi-agent systems that guarantees stability regardless of the number of agents, advancing robustness analysis under uncertainty.

Findings

Bound on $6$ norm independent of agent count

Comparison with polynomial chaos expansion methods

Numerical validation on 1D and 2D systems

Abstract

We consider control strategies for large-scale interacting agent systems under uncertainty. The particular focus is on the design of robust controls that allow to bound the variance of the controlled system over time. To this end we consider $\mathcal{H}_\infty$ control strategies on the agent and mean field description of the system. We show a bound on the $\mathcal{H}_\infty$ norm for a stabilizing controller independent on the number of agents. Furthermore, we compare the new control with existing approaches to treat uncertainty by generalized polynomial chaos expansion. Numerical results are presented for one-dimensional and two-dimensional agent systems.