Mayer control problem with probabilistic uncertainty on initial positions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Marigonda, Antonio¹  Quincampoix, Marc² 

[1] Univ Verona, Dept Comp Sci, Str Le Grazie 15, I-37134 Verona, Italy

[2] Univ Brest, CNRS, UMR 6205, Lab Math Bretagne Atlantique, 6 Ave Victor Le Gorgeu,CS 93837, F-29238 Brest 3, France

关键词: Differential games;    Optimal transport;    Hamilton-Jacobi-Bellman equation;   

DOI  :  10.1016/j.jde.2017.11.014

来源: Elsevier

【 摘 要 】

In this paper we introduce and study an optimal control problem in the Mayer's form in the space of probability measures on R-n 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 R-d and by a vector-valued measure on R-d, 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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free