Transport maps as flows of control-affine systems
Optimization and Control
2025-06-23 v4
Abstract
We consider the problem of transporting \nota{one probability measure into another through} the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop controls is a sufficient condition for the existence of time-varying feedback controls such that the -time flow of the system is the optimal transport map for the quadratic cost.
Keywords
Cite
@article{arxiv.2404.12793,
title = {Transport maps as flows of control-affine systems},
author = {Marco Caponigro and Arianna Vicari},
journal= {arXiv preprint arXiv:2404.12793},
year = {2025}
}