Sinkhorn MPC: Model predictive optimal transport over dynamical systems
Abstract
We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over a dynamical system, which is challenging due to its high computational cost. In this paper, we propose Sinkhorn MPC, which is a dynamical transport algorithm combining model predictive control and the so-called Sinkhorn algorithm. The notable feature of the proposed method is that it achieves cost-effective transport in real time by performing control and transport planning simultaneously. In particular, for linear systems with an energy cost, we reveal the fundamental properties of Sinkhorn MPC such as ultimate boundedness and asymptotic stability.
Cite
@article{arxiv.2203.08415,
title = {Sinkhorn MPC: Model predictive optimal transport over dynamical systems},
author = {Kaito Ito and Kenji Kashima},
journal= {arXiv preprint arXiv:2203.08415},
year = {2022}
}
Comments
6 pages, 2 figures, accepted to the 2022 American Control Conference