Publications

Authors:

Marigonda, Antonio; Quincampoix, Marc

Title:

Mayer control problem with probabilistic uncertainty on initial positions

Year:

2018

Type of item:

Articolo in Rivista

Tipologia ANVUR:

Articolo su rivista

Language:

Inglese

Format:

A Stampa

Referee:

Sì

Name of journal:

Journal of Differential Equations

ISSN of journal:

0022-0396

N° Volume:

264

Number or Folder:

5

:

Elsevier

Page numbers:

3212-3252

Keyword:

Differential games, Optimal transport, Hamilton–Jacobi–Bellman equation

Short description of contents:

In this paper we introduce and study an optimal control problem in the Mayer's form in the space of probability measures on Rn endowed with the Wasserstein distance. Our aim is to study optimality conditions when the knowledge of the initial state and velocity is subject to some uncertainty, which are modeled by a probability measure on Rd and by a vector-valued measure on Rd, respectively. We provide a characterization of the value function of such a problem as unique solution of an Hamilton-Jacobi-Bellman equation in the space of measures in a suitable viscosity sense. Some applications to a pursuit-evasion game with uncertainty in the state space is also discussed, proving the existence of a value for the game.

Web page:

http://www.sciencedirect.com/science/article/pii/S0022039617306046

Product ID:

100085

Handle IRIS:

11562/972232

Last Modified:

November 27, 2022

Bibliographic citation:

Marigonda, Antonio; Quincampoix, Marc, Mayer control problem with probabilistic uncertainty on initial positions «Journal of Differential Equations» , vol. 264 , n. 5 , 2018 , pp. 3212-3252

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