Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: Equivalence and Gamma-convergence
By Giulia Cavagnari, S. Lisini, Carlo Orrieri, Giuseppe Savar'e. Journal of Differential Equations, 2020
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This paper is devoted to the study of multi-agent deterministic optimal control problems. We initially provide a thorough analysis of the Lagrangian, Eulerian and Kantorovich formulations of the problems, as well as of their relaxations. Then we exhibit some equivalence results among the various representations and compare the respective value functions. To do it, we combine techniques and ideas from optimal transportation, 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. To that purpose we prove an empirical version of the Superposition Principle and obtain suitable Gamma-convergence results for the controlled systems.
Subfields: Computational Theory and Mathematics, Finance, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/dab305922409cc7f67cc089fa5ac2d5173b7cee9
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Citations in the corpus
- Necessary Optimality Conditions for Optimal Control Problems in Wasserstein Spaces (2021, background): “The first contributions on this topic [25,26] were concerned with the rigorous convergence of discrete multi-agent optimal controls towards their infinitedimensional counterparts (see also the more recent contributions [18,25]), which provides a constructivewayof recovering the existence of optimal ”