# On the equivalence between static and dynamic optimal transport governed by linear control systems

arXiv: https://arxiv.org/abs/2505.17570 · HTML: https://mlsanity.com/paper/2505.17570/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2025.

## Built on by (most cited first, 1 of 1)

- [From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties](https://mlsanity.com/paper/2507.11387/) (2025)

## Abstract (arXiv)

In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on ℝd×ℝd derived from suitable variational problems, we show the equivalence between the static and dynamic versions of the corresponding transport problems. Our analysis is constructive in nature and relies on functional analytic properties of the end-point map and the fine properties of the optimal control functions. These lead to some new quantitative estimates which play a crucial role in our investigation.