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

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Authors : Savaré, Giuseppe (Author of the conference)
CIRM (Publisher )

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Abstract : 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)

Keywords : Wasserstein distance; optimal control; mean-field optimal control; gamma convergence

MSC Codes :
49Q22 - Optimal transportation
49N80 - Mean field games and control

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

    Information on the Video

    Film maker : Recanzone, Luca
    Language : English
    Available date : 30/04/2024
    Conference Date : 08/04/2024
    Subseries : Research School
    arXiv category : Optimization and Control ; Analysis of PDEs
    Mathematical Area(s) : Analysis and its Applications ; Control Theory & Optimization ; Dynamical Systems & ODE ; PDE
    Format : MP4 (.mp4) - HD
    Video Time : 00:46:17
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-04-08_Savare.mp4

Information on the Event

Event Title : 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
Event Organizers : Carrillo, José Antonio ; Esposito, Antonio ; Gómez-Castro, David ; Nouri, Anne
Dates : 08/04/2024 - 12/04/2024
Event Year : 2024
Event URL : https://conferences.cirm-math.fr/3049.html

Citation Data

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

See Also

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



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