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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)

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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

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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