# Density Steering of Gaussian Mixture Models for Discrete-Time Linear Systems

arXiv: https://arxiv.org/abs/2311.08500 · HTML: https://mlsanity.com/paper/2311.08500/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2023.

## Built on by (most cited first, 2 of 2)

- [Linear Mixture Distributionally Robust Markov Decision Processes](https://mlsanity.com/paper/2505.18044/) (2025)
- [Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance](https://mlsanity.com/paper/2508.06052/) (2025)

## Abstract (arXiv)

In this paper, we study the finite-horizon optimal density steering problem for discrete-time stochastic linear dynamical systems. Specifically, we focus on steering probability densities represented as Gaussian mixture models which are known to give good approximations for general smooth probability density functions. We then revisit the covariance steering problem for Gaussian distributions and derive its optimal control policy. Subsequently, we propose a randomized policy to enhance the numerical tractability of the problem and demonstrate that under this policy the state distribution remains a Gaussian mixture. By leveraging these results, we reduce the Gaussian mixture steering problem to a linear program. We also discuss the problem of steering general distributions using Gaussian mixture approximations. Finally, we present results of non-trivial numerical experiments and demonstrate that our approach can be applied to general distribution steering problems.