Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems

Abstract: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.

Optimization and Control (math.OC); Machine Learning (cs.LG); Multiagent Systems (cs.MA); Systems and Control (eess.SY)

arXiv:2607.09139 [math.OC]

(or arXiv:2607.09139v2 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2607.09139 Focus to learn more arXiv-issued DOI via DataCite

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