# Learning Robust Data-based LQG Controllers from Noisy Data

arXiv: https://arxiv.org/abs/2305.01417 · HTML: https://mlsanity.com/paper/2305.01417/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2023.

## Built on by (most cited first, 3 of 3)

- [Regret Analysis of Policy Optimization over Submanifolds for Linearly Constrained Online LQG](https://mlsanity.com/paper/2403.08553/) (2024)
- [Direct Data Driven Control Using Noisy Measurements](https://mlsanity.com/paper/2505.06407/) (2025)
- [A PAC-Bayes Approach for Controlling Unknown Linear Discrete-time Systems](https://mlsanity.com/paper/2605.10493/) (2026)

## Abstract (arXiv)

This paper addresses the joint state estimation and control problems for unknown linear time-invariant systems subject to both process and measurement noise. The aim is to redesign the linear quadratic Gaussian (LQG) controller based solely on data. The LQG controller comprises a linear quadratic regulator (LQR) and a steady-state Kalman observer; while the data-based LQR design problem has been previously studied, constructing the Kalman gain and the LQG controller from noisy data presents a novel challenge. In this work, a data-based formulation for computing the steady-state Kalman gain is proposed based on semi-definite programming (SDP) using some noise-free input-state-output data. Additionally, a data-based LQG controller is developed, which is shown to be equivalent to the model-based LQG controller. For cases where offline data are corrupted by noise, a robust data-based observer gain is constructed by tackling a relaxed SDP. The proposed controllers are proven to achieve robust global exponential stability (RGES) for state estimation and input-to-state practical stability (ISpS) under standard conditions. Finally, numerical tests are conducted to validate the proposed controllers' correctness and effectiveness.