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

  • Ripon C. Sarker
  • Abhishek Halder
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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.

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Cite

BibTeXRIS
BibTeX
@misc{sarker2026control,
  title = {{Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems}},
  author = {Ripon C. Sarker and Abhishek Halder},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.09139},
  eprint = {2607.09139},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.09139},
}
RIS
TY  - UNPB
TI  - Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems
AU  - Ripon C. Sarker
AU  - Abhishek Halder
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2607.09139
UR  - https://arxiv.org/abs/2607.09139
AB  - 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.
ER  -