Reachability for multiagent control systems via Lyapunov functions

This paper concerns the problem of reachability of a given state for a multiagent control system in R ᵈ. In such a system, at every time, each agent can choose their velocity which depends both on their position and on the position of the whole crowd of agents (modeled by a probability measure on 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.