Entropic Model Predictive Optimal Transport for Underactuated Linear Systems

TL;DR

This paper extends entropic optimal transport methods to underactuated linear systems, enabling efficient dynamical transport with proven convergence, broadening applicability beyond fully actuated systems.

Contribution

It introduces a generalized approach for optimal transport in underactuated linear systems, overcoming previous invertibility limitations and establishing convergence guarantees.

Findings

Method successfully applied to controllable linear systems.

Demonstrates convergence properties in numerical examples.

Broadens the scope of optimal transport for underactuated systems.

Abstract

This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform efficient dynamical transport of agents. However, the proposed method requires the invertibility of input matrices, which severely limits its applicability. To resolve this issue, we extend the method to (possibly underactuated) controllable linear systems. In addition, we ensure the convergence properties of the method for general controllable linear systems. The effectiveness of the proposed method is demonstrated by a numerical example.