# Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise

arXiv: https://arxiv.org/abs/2205.05119 · HTML: https://mlsanity.com/paper/2205.05119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 10 May 2022.

## Builds on (most cited first, 10 of 10)

- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Finite Sample Analysis of Stochastic System Identification](https://mlsanity.com/paper/1903.09122/) (2019)
- [Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems](https://mlsanity.com/paper/2003.11227/) (2020)
- [Sample Complexity Lower Bounds for Linear System Identification](https://mlsanity.com/paper/1903.10343/) (2019)
- [Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems](https://mlsanity.com/paper/2011.09929/) (2020)
- [Learning robust control for LQR systems with multiplicative noise via policy gradient](https://mlsanity.com/paper/1905.13547/) (2019)
- [Robust Learning-Based Control via Bootstrapped Multiplicative Noise](https://mlsanity.com/paper/2002.10069/) (2020)
- [Sample Complexity of the Robust LQG Regulator with Coprime Factors Uncertainty](https://mlsanity.com/paper/2109.14164/) (2021)

## Built on by (most cited first, 1 of 1)

- [Direct Data Driven Control Using Noisy Measurements](https://mlsanity.com/paper/2505.06407/) (2025)

## Abstract (arXiv)

We propose a robust data-driven output feedback control algorithm that explicitly incorporates inherent finite-sample model estimate uncertainties into the control design. The algorithm has three components: (1) a subspace identification nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method comprising a coupled optimal dynamic output feedback filter and controller with multiplicative noise. A key advantage of the proposed approach is that the system identification and robust control design procedures both use stochastic uncertainty representations, so that the actual inherent statistical estimation uncertainty directly aligns with the uncertainty the robust controller is being designed against. Moreover, the control design method accommodates a highly structured uncertainty representation that can capture uncertainty shape more effectively than existing approaches. We show through numerical experiments that the proposed robust data-driven output feedback controller can significantly outperform a certainty equivalent controller on various measures of sample complexity and stability robustness.