Sinkhorn MPC: Model predictive optimal transport over dynamical systems

TL;DR

This paper introduces Sinkhorn MPC, a real-time control algorithm that combines model predictive control and Sinkhorn algorithm to efficiently solve optimal transport problems over dynamical systems, ensuring stability and boundedness.

Contribution

It presents a novel method integrating Sinkhorn algorithm with MPC for cost-effective, real-time optimal transport over dynamical systems, with theoretical stability guarantees.

Findings

Achieves real-time cost-effective transport planning.

Ensures ultimate boundedness and asymptotic stability for linear systems.

Demonstrates effectiveness through theoretical analysis.

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.