Mean-Field Optimal Control of Continuity Equations and Differential Inclusions

TL;DR

This paper introduces a novel framework for multi-agent control in mean-field settings using differential inclusions in Wasserstein spaces, enabling a unified analysis and solution correspondence.

Contribution

It develops a new definition of differential inclusions in Wasserstein spaces, extending classical theories to mean-field control problems and establishing solution-control system equivalence.

Findings

Framework successfully models multi-agent control problems.

Proves correspondence between differential inclusions and control solutions.

Demonstrates application on leader-follower evacuation scenario.

Abstract

In this article, we propose a new unifying framework for the investigation of multi-agent control problems in the mean-field setting. Our approach is based on a new definition of differential inclusions for continuity equations formulated in the Wasserstein spaces of optimal transport. The latter allows to extend several known results of the classical theory of differential inclusions, and to prove an exact correspondence between solutions of differential inclusions and control systems. We show its appropriateness on an example of leader-follower evacuation problem.