控制拉盖尔镶嵌：控制系统上的半离散最优传输
Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems
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中文总结 AI 辅助
研究最优控制智能体从紧支绝对连续源到离散目标测度的最优传输，当地础成本满足扭转条件时，最优传输映射由状态空间的拉盖尔镶嵌给出，推广出控制拉盖尔镶嵌并通过两种基础成本进行说明。
中文摘要 AI 辅助
我们研究了从紧支绝对连续源到离散目标测度的最优控制智能体的最优传输。传输的基础成本由智能体运动的最优成本诱导。当地础成本满足扭转条件时，最优传输映射几乎处处由状态空间的拉盖尔镶嵌给出。我们将这种拉盖尔镶嵌的控制理论推广称为控制拉盖尔镶嵌（CLT），并通过由具有最小能量和最短时间目标的线性控制智能体诱导的两种基础成本进行说明。
英文摘要
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.
发表机构
- Department of Aerospace Engineering, Iowa State University（航空航天工程系，爱荷华州立大学）
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