In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control problems in the Wasserstein space of probability measures. The dynamics is described by a transport equation with non-local velocities which are affine in the control, and is subject to end-point and running state constraints. Building on our previous work, we combine the classical method of needle-variations from geometric control theory and the metric differential structure of the Wasserstein spaces to obtain a maximum principle formulated in the so-called Gamkrelidze form.
Accepté le :
DOI : 10.1051/cocv/2019044
Keywords: Pontryagin Maximum Principle, Wasserstein spaces, metric differential calculus, needle-like variations, state constraints
Bonnet, Benoît 1
@article{COCV_2019__25__A52_0,
author = {Bonnet, Beno{\^\i}t},
title = {A {Pontryagin} {Maximum} {Principle} in {Wasserstein} spaces for constrained optimal control problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2019},
publisher = {EDP Sciences},
volume = {25},
doi = {10.1051/cocv/2019044},
zbl = {1442.49025},
mrnumber = {4019758},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2019044/}
}
TY - JOUR AU - Bonnet, Benoît TI - A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2019044/ DO - 10.1051/cocv/2019044 LA - en ID - COCV_2019__25__A52_0 ER -
%0 Journal Article %A Bonnet, Benoît %T A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2019044/ %R 10.1051/cocv/2019044 %G en %F COCV_2019__25__A52_0
Bonnet, Benoît. A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 52. doi: 10.1051/cocv/2019044
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