Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems | Vidéo | Carmin.tv

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Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems

By Giuseppe Savaré

Appears in collection : Aggregation-Diffusion Equations & Collective Behavior: Analysis, Numerics and Applications / Conférence Chaire Jean Morlet: Equations d'agrégation-diffusion et comportement collectif: Analyse, schémas numériques et applications

We discuss the natural Lagrangian and Eulerian formulations of multi-agent deterministic optimal control problems, analyzing their relations with a novel Kantorovich formulation. We exhibit some equivalence results among the various representations and compare the respective value functions, by combining techniques and ideas from optimal transport, control theory, Young measures and evolution equations in Banach spaces. We further exploit the connections among Lagrangian and Eulerian descriptions to derive consistency results as the number of particles/agents tends to infinity. (In collaboration with Giulia Cavagnari, Stefano Lisini and Carlo Orrieri)

Information about the video

Date of recording 08/04/2024
Date of publication 30/04/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20160003
Cite this video Savaré, Giuseppe (08/04/2024). Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20160003
URL https://dx.doi.org/10.24350/CIRM.V.20160003

Domain(s)

Bibliography

CAVAGNARI, Giulia, LISINI, Stefano, ORRIERI, Carlo, et al. Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: equivalence and gamma-convergence. Journal of Differential Equations, 2022, vol. 322, p. 268-364. - https://doi.org/10.1016/j.jde.2022.03.019

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/3049/Slides/Giuseppe_Savare_CIRM2024.pdf

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