Mean-field control barrier functions for stochastic multi-agent systems

TL;DR

This paper develops mean-field control barrier functions for stochastic multi-agent systems, enabling safety guarantees in large-scale, stochastic environments by addressing the gap in Fokker-Planck equation applications.

Contribution

It introduces a novel framework for mean-field control barrier functions tailored to stochastic dynamics governed by Fokker-Planck equations, filling a key gap in the literature.

Findings

Provides bounded stability guarantees under safety corrections

Demonstrates effectiveness through numerical simulations in coverage and shepherding scenarios

Enables safe control of large-scale stochastic multi-agent systems

Abstract

Many applications involving multi-agent systems require fulfilling safety constraints. Control barrier functions offer a systematic framework to enforce forward invariance of safety sets. Recent work extended this paradigm to mean-field scenarios, where the number of agents is large enough to make density-space descriptions a reasonable workaround for the curse of dimensionality. However, an open gap in the recent literature concerns the development of mean-field control barrier functions for Fokker-Planck (advection-diffusion) equations. In this work, we address this gap, enabling safe mean-field control of agents with stochastic microscopic dynamics. We provide bounded stability guarantees under safety corrections and corroborate our results through numerical simulations in two representative scenarios, coverage and shepherding control of multi-agent systems.