# Data-driven distributionally robust LQR with multiplicative noise

arXiv: https://arxiv.org/abs/1912.09990 · HTML: https://mlsanity.com/paper/1912.09990/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2019.

## Built on by (most cited first, 7 of 7)

- [A Distributionally Robust Approach to Regret Optimal Control using the Wasserstein Distance](https://mlsanity.com/paper/2304.06783/) (2023)
- [Direct Data-Driven Discounted Infinite Horizon Linear Quadratic Regulator with Robustness Guarantees](https://mlsanity.com/paper/2409.10703/) (2024)
- [Distributionally Robust Optimization using Cost-Aware Ambiguity Sets](https://mlsanity.com/paper/2303.09408/) (2023)
- [Sample Complexity of Linear Quadratic Regulator Without Initial Stability](https://mlsanity.com/paper/2502.14210/) (2025)
- [Risk-Aware Safe Reinforcement Learning for Control of Stochastic Linear Systems](https://mlsanity.com/paper/2505.09734/) (2025)
- [Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets](https://mlsanity.com/paper/2512.10906/) (2025)
- [On Reward-Balancing Methods for Reinforcement Learning](https://mlsanity.com/paper/2604.20433/) (2026)

## Abstract (arXiv)

We present a data-driven method for solving the linear quadratic regulator problem for systems with multiplicative disturbances, the distribution of which is only known through sample estimates. We adopt a distributionally robust approach to cast the controller synthesis problem as semidefinite programs. Using results from high dimensional statistics, the proposed methodology ensures that their solution provides mean-square stabilizing controllers with high probability even for low sample sizes. As sample size increases the closed-loop cost approaches that of the optimal controller produced when the distribution is known. We demonstrate the practical applicability and performance of the method through a numerical experiment.