Reachability for multiagent control systems via Lyapunov functions

Abstract

This paper concerns the problem of reachability of a given state for a multiagent control system in ${\mathbb{R}}^d$. In such a system, at every time each agent can choose his/her velocity which depends both on his/her position and on the position of the whole crowd of agents (modeled by a probability measure on ${\mathbb{R}}^d$). The main contribution of the paper is to study the above reachability problem with a given rate of attainability through a Lyapunov method adapted to the Wasserstein space of probability measures. As a byproduct we obtain a new comparison result for viscosity solutions of Hamilton Jacobi equations in the Wasserstein space.

This is the author accepted manuscript of an article published in Communications on Pure and Applied Analysis