论文标题
Lagrangian，Eulerian和Kantorovich多代理最佳控制问题的公式
Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: Equivalence and Gamma-convergence
论文作者
论文摘要
本文致力于研究多代理确定性最佳控制问题。我们最初对问题的拉格朗日，欧拉和坎托维奇的表述进行了详尽的分析，以及它们的放松。然后，我们在各种表示之间表现出一些等效的结果，并比较各自的价值函数。为此，我们结合了Banach空间中最佳运输，控制理论，年轻措施和进化方程的技术和思想。我们进一步利用拉格朗日和欧拉描述之间的连接以得出一致性结果，因为粒子/代理的数量倾向于无穷大。为此，我们证明了叠加原理的经验版本，并为受控系统获得合适的伽马连接结果。
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.
