Work

Reachability for multiagent control systems via Lyapunov functions

Year: 2025

Type: article

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 their velocity which depends both on their 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.

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2025100

Authors: Giulia Cavagnari, Marc Quincampoix

Institutions: Centre National de la Recherche Scientifique, Université de Bretagne Occidentale, Laboratoire de Mathématiques de Bretagne Atlantique

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Agence Nationale de la Recherche

Awards: COntrol on Stratified Structures, G465505792, G5488169599