# Wasserstein Distributionally Robust Control of Partially Observable Linear Stochastic Systems

arXiv: https://arxiv.org/abs/2212.04644 · HTML: https://mlsanity.com/paper/2212.04644/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2022.

## Built on by (most cited first, 4 of 4)

- [Policy Evaluation in Distributional LQR](https://mlsanity.com/paper/2303.13657/) (2023)
- [Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning](https://mlsanity.com/paper/2510.10214/) (2025)
- [Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets](https://mlsanity.com/paper/2512.10906/) (2025)
- [Data-driven robust Markov decision processes on Borel spaces: performance guarantees via an axiomatic approach](https://mlsanity.com/paper/2603.08979/) (2026)

## Abstract (arXiv)

Distributionally robust control (DRC) aims to effectively manage distributional ambiguity in stochastic systems. While most existing works address inaccurate distributional information in fully observable settings, we consider a partially observable DRC problem for discrete-time linear systems using the Wasserstein metric. For a tractable solution, we propose a novel approximation method exploiting the Gelbrich bound of Wasserstein distance. Using techniques from modern distributionally robust optimization, we derive a closed-form expression for the optimal control policy and a tractable semidefinite programming problem for the worst-case distribution policy in both finite-horizon and infinite-horizon average-cost settings. The proposed method features several salient theoretical properties, such as a guaranteed cost property and a probabilistic out-of-sample performance guarantee, demonstrating the distributional robustness of our controller. Furthermore, the resulting controller is shown to ensure the closed-loop stability of the mean-state system. The empirical performance of our method is tested through numerical experiments on a power system frequency control problem.