Attainability property for a probabilistic target in wasserstein spaces

Giulia Cavagnari; Antonio Marigonda

doi:10.3934/dcds.2020300

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2021, Volume 41, Issue 2: 777-812. Doi: 10.3934/dcds.2020300

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Attainability property for a probabilistic target in wasserstein spaces

Giulia Cavagnari^1, , and
Antonio Marigonda^2,

1.
Politecnico di Milano, Dipartimento di Matematica "F. Brioschi", Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
2.
University of Verona, Department of Computer Science, Strada Le Grazie 15, I-37134 Verona, Italy

^* Corresponding author: Giulia Cavagnari
^* Corresponding author: Giulia Cavagnari

Received: April 2019

Revised: April 2020

Early access: August 2020

Published: February 2021

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Abstract

In this paper we establish an attainability result for the minimum time function of a control problem in the space of probability measures endowed with Wasserstein distance. The dynamics is provided by a suitable controlled continuity equation, where we impose a nonlocal nonholonomic constraint on the driving vector field, which is assumed to be a Borel selection of a given set-valued map. This model can be used to describe at a macroscopic level a so-called multiagent system made of several possible interacting agents.

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Mathematics Subject Classification: Primary: 34A60; Secondary: 49J15, 49J53, 90C56.

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