Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance

TL;DR

This paper introduces a data-driven method for density steering using the Gromov-Wasserstein distance, enabling control of unknown linear systems to match target distributions based on experimental data.

Contribution

It formulates the density steering problem as a difference-of-convex program and demonstrates an efficient solution approach with numerical validation.

Findings

Effective density control of unknown linear systems.

Tractable solution via difference-of-convex programming.

Validated with numerical experiments.

Abstract

We tackle the data-driven chance-constrained density steering problem using the Gromov-Wasserstein metric. The underlying dynamical system is an unknown linear controlled recursion, with the assumption that sufficiently rich input-output data from pre-operational experiments are available. The initial state is modeled as a Gaussian mixture, while the terminal state is required to match a specified Gaussian distribution. We reformulate the resulting optimal control problem as a difference-of-convex program and show that it can be efficiently and tractably solved using the DC algorithm. Numerical results validate our approach through various data-driven schemes.