# Distributionally Robust Linear Quadratic Control

arXiv: https://arxiv.org/abs/2305.17037 · HTML: https://mlsanity.com/paper/2305.17037/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2023.

## Built on by (most cited first, 8 of 8)

- [On the Foundation of Distributionally Robust Reinforcement Learning](https://mlsanity.com/paper/2311.09018/) (2023)
- [Distributionally Robust Free Energy Principle for Decision-Making](https://mlsanity.com/paper/2503.13223/) (2025)
- [Distributionally Robust Policy and Lyapunov-Certificate Learning](https://mlsanity.com/paper/2404.03017/) (2024)
- [A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set](https://mlsanity.com/paper/2405.20124/) (2024)
- [Learning Optimal Distributionally Robust Stochastic Control in Continuous State Spaces](https://mlsanity.com/paper/2406.11281/) (2024)
- [Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets](https://mlsanity.com/paper/2512.10906/) (2025)
- [Policy Gradient for Continuous-Time Robust Markov Decision Processes](https://mlsanity.com/paper/2606.04335/) (2026)
- [Learning Perturbation Robust Policies for LLM Agents with Stable Optimization](https://mlsanity.com/paper/2609.34064/) (2026)

## Abstract (arXiv)

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations, subject to additive noise, with the goal of minimizing a quadratic cost function for the state and control variables. In this work, we consider a generalization of the discrete-time, finite-horizon LQG problem, where the noise distributions are unknown and belong to Wasserstein ambiguity sets centered at nominal (Gaussian) distributions. The objective is to minimize a worst-case cost across all distributions in the ambiguity set, including non-Gaussian distributions. Despite the added complexity, we prove that a control policy that is linear in the observations is optimal for this problem, as in the classic LQG problem. We propose a numerical solution method that efficiently characterizes this optimal control policy. Our method uses the Frank-Wolfe algorithm to identify the least-favorable distributions within the Wasserstein ambiguity sets and computes the controller's optimal policy using Kalman filter estimation under these distributions.