论文标题
$ 1 $ - 二维的多代理最佳控制，汇总和距离限制：定性属性和均值范围限制
$1$-dimensional multi-agent optimal control with aggregation and distance constraints: qualitative properties and mean-field limit
论文作者
论文摘要
在本文中，我们考虑了具有确定性动态的大量相互作用的药物的最佳控制问题，在维度1中汇总了对相互距离的潜在和限制。我们研究了有限试剂的最佳轨迹的周期性和定性特性，以及对解决方案支撑的压缩和距离饱和度的压缩的最佳轨迹的最佳轨迹。此外，我们通过$γ$ - 融合的结果证明，平均场最佳控制问题的一致性具有密度约束，并具有相应的潜在有限剂一号，我们推断了极限问题的时间周期性平衡的一些定性结果。
In this paper we consider an optimal control problem for a large population of interacting agents with deterministic dynamics, aggregating potential and constraints on reciprocal distances, in dimension 1. We study existence and qualitative properties of periodic in time optimal trajectories of the finite agents optimal control problem, with particular interest on the compactness of the solutions' support and on the saturation of the distance constraint. Moreover, we prove, through a $Γ$-convergence result, the consistency of the mean-field optimal control problem with density constraints with the corresponding underlying finite agent one and we deduce some qualitative results for the time periodic equilibria of the limit problem.
