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

Excerpt

arXiv:2607.09139v2 Announce Type: replace-cross 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 generaliz