A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems

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...

Full description

Saved in:
Bibliographic Details
Published inESAIM. Control, optimisation and calculus of variations Vol. 25; no. 52; p. 52
Main Author Bonnet, Benoît
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 2019
Subjects
49K20
49K27
58E25
Analysis of PDEs
Constraints
Control theory
Differential geometry
Mathematics
Maximum principle
metric differential calculus
needle-like variations
Optimal control
Optimization and Control
Pontryagin Maximum Principle
state constraints
Transport equations
Wasserstein spaces
metric differential calculus
needle-like variations
Pontryagin Maximum Principle
Wasserstein spaces
state constraints
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ark:/67375/80W-HZMSB5J4-2
istex:CEE4F0E8FCE9B07C2324A085143EA117F6041B97
This research is partially supported by the Padua University grant SID 2018 “Controllability, stabilizability and infimun gaps for control systems”, prot. BIRD 187147. The author was supported by the Archimède Labex (ANR-11-LABX-0033), by the A*MIDEX project (ANR- 11-IDEX-0001-02), funded by the “Investissements d'Avenir” French Government program managed by the French National Research Agency (ANR), and by the SRGI ANR Grant ANR-15-CE40-0018.
publisher-ID:cocv180153
href:https://www.esaim-cocv.org/articles/cocv/abs/2019/01/cocv180153/cocv180153.html
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2019044