# Direct Data Driven Control Using Noisy Measurements

arXiv: https://arxiv.org/abs/2505.06407 · HTML: https://mlsanity.com/paper/2505.06407/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 9 May 2025.

## Builds on (most cited first, 13 of 13)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Data informativity: a new perspective on data-driven analysis and control](https://mlsanity.com/paper/1908.00468/) (2019)
- [Bridging direct & indirect data-driven control formulations via regularizations and relaxations](https://mlsanity.com/paper/2101.01273/) (2021)
- [Low-complexity Learning of Linear Quadratic Regulators from Noisy Data](https://mlsanity.com/paper/2005.01082/) (2020)
- [Model-free optimal control of discrete-time systems with additive and multiplicative noises](https://mlsanity.com/paper/2008.08734/) (2020)
- [Behavioral Feedback for Optimal LQG Control](https://mlsanity.com/paper/2204.00702/) (2022)
- [Learning Robust Data-based LQG Controllers from Noisy Data](https://mlsanity.com/paper/2305.01417/) (2023)
- [Direct data-driven control of LTV systems](https://mlsanity.com/paper/2111.02342/) (2021)
- [Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise](https://mlsanity.com/paper/2205.05119/) (2022)
- [Direct Data-Driven Discounted Infinite Horizon Linear Quadratic Regulator with Robustness Guarantees](https://mlsanity.com/paper/2409.10703/) (2024)
- [Data-Driven Structured Robust Control of Linear Systems](https://mlsanity.com/paper/2411.11542/) (2024)

## Abstract (arXiv)

This paper presents a novel direct data-driven control framework for solving the linear quadratic regulator (LQR) under disturbances and noisy state measurements. The system dynamics are assumed unknown, and the LQR solution is learned using only a single trajectory of noisy input-output data while bypassing system identification. Our approach guarantees mean-square stability (MSS) and optimal performance by leveraging convex optimization techniques that incorporate noise statistics directly into the controller synthesis. First, we establish a theoretical result showing that the MSS of an uncertain data-driven system implies the MSS of the true closed-loop system. Building on this, we develop a robust stability condition using linear matrix inequalities (LMIs) that yields a stabilizing controller gain from noisy measurements. Finally, we formulate a data-driven LQR problem as a semidefinite program (SDP) that computes an optimal gain, minimizing the steady-state covariance. Extensive simulations on benchmark systems -- including a rotary inverted pendulum and an active suspension system -- demonstrate the superior robustness and accuracy of our method compared to existing data-driven LQR approaches. The proposed framework offers a practical and theoretically grounded solution for controller design in noise-corrupted environments where system identification is infeasible.