SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1183-1206, April 2024.
Abstract. We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces results from two ingredients: (i) the solution of dynamic programming in the “ground space” (i.e., the space on which the probability measures live) and (ii) the solution of an optimal transport problem. From a multi-agent control perspective, a separation principle holds: “low-level control of the agents of the fleet” (how does one reach the destination?) and “fleet-level control” (who goes where?) are decoupled.

中文翻译：

---

通过最优传输的概率空间动态规划

SIAM 控制与优化杂志，第 62 卷，第 2 期，第 1183-1206 页，2024 年 4 月
。摘要。我们研究概率空间中的离散时间有限范围最优控制问题，其中系统的状态是概率测度。我们表明，在许多情况下，概率空间中的动态规划的解决方案由两个成分产生：（i）“地面空间”（即概率测量所在的空间）中的动态规划的解决方案和（ii） ）最优运输问题的解决方案。从多智能体控制的角度来看，分离原则成立：“车队智能体的低级控制”（如何到达目的地？）和“车队级控制”（谁去哪里？）是解耦的。