用控制理论推广拉盖尔剖分，解决受控智能体最优运输问题
Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems
- 基于控制系统的最优代价定义运输成本，构建控制拉盖尔剖分
- 在最小能量与最短时间目标下，成功实现状态空间的精确剖分
- 适用于多智能体路径规划与分布式控制，理论价值高
研究从紧支撑绝对连续源到离散目标测度的受控智能体最优运输问题。运输的基代价由智能体运动的最优代价诱导。当该基代价满足扭动条件时，最优运输映射几乎处处可表示为状态空间的拉盖尔剖分。我们称这种控制理论推广为控制拉盖尔剖分（CLT），并在两类由线性受控智能体在最小能量和最短时间目标下诱导的基代价中进行了说明。
原文摘要 · Abstract (English)
We study the optimal transport of optimally controlled agents from a compactly supported absolutely continuous source to a discrete target measure. The ground cost for the transport is induced by the optimal cost of the agents' motion. When this ground cost satisfies the twist condition, the optimal transport map is given almost everywhere in terms of a Laguerre tessellation of the state space. We refer to this control-theoretic generalization of Laguerre tessellation as Control Laguerre Tessellation (CLT), and illustrate it for two ground costs induced by linear controlled agents with minimum energy and minimum time objectives.
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