Unbalanced Optimal Transport and Density Control for Discrete-Time Linear Systems
Abstract
This article studies unbalanced optimal transport (UOT) and its dynamical extension, unbalanced density control (UDC), for a class of constrained discrete-time linear systems. UOT compares measures with unequal total mass by balancing transport cost and fidelity to reference measures, while UDC incorporates system dynamics and constraints into this framework. Focusing on Gaussian references and discrete-time linear systems, we show that both problems admit globally optimal convex formulations, analogous to covariance steering. A numerical experiment is provided to illustrate our approach.
Keywords
Cite
@article{arxiv.2605.06391,
title = {Unbalanced Optimal Transport and Density Control for Discrete-Time Linear Systems},
author = {Haruto Nakashima and Siddhartha Ganguly and Kenji Kashima},
journal= {arXiv preprint arXiv:2605.06391},
year = {2026}
}
Comments
To appear in the Proceedings of MTNS 2026 (extended abstracts). Submitted on February 15, 2026; accepted on April 20, 2026. A significantly expanded version containing additional theoretical results, complete proofs, and numerical experiments, is available at: arXiv:2605.04246v1