# Data-Driven Continuous-Time Linear Quadratic Regulator via Closed-Loop and Reinforcement Learning Parameterizations

arXiv: https://arxiv.org/abs/2604.27922 · HTML: https://mlsanity.com/paper/2604.27922/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 16 of 16)

- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [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)
- [Policy Gradient-based Algorithms for Continuous-time Linear Quadratic Control](https://mlsanity.com/paper/2006.09178/) (2020)
- [From noisy data to feedback controllers: non-conservative design via a matrix S-lemma](https://mlsanity.com/paper/2006.00870/) (2020)
- [Data-Enabled Policy Optimization for Direct Adaptive Learning of the LQR](https://mlsanity.com/paper/2401.14871/) (2024)
- [Low-complexity Learning of Linear Quadratic Regulators from Noisy Data](https://mlsanity.com/paper/2005.01082/) (2020)
- [Robust data-driven state-feedback design](https://mlsanity.com/paper/1909.04314/) (2019)
- [Data-Driven LQR Control Design](https://mlsanity.com/paper/1807.03263/) (2018)
- [On the Certainty-Equivalence Approach to Direct Data-Driven LQR Design](https://mlsanity.com/paper/2109.06643/) (2021)
- [Regularization for Covariance Parameterization of Direct Data-Driven LQR Control](https://mlsanity.com/paper/2503.02985/) (2025)
- [A Matrix Finsler's Lemma with Applications to Data-Driven Control](https://mlsanity.com/paper/2103.13461/) (2021)
- [Data-enabled Policy Optimization for the Linear Quadratic Regulator](https://mlsanity.com/paper/2303.17958/) (2023)
- [When sampling works in data-driven control: Informativity for stabilization in continuous time](https://mlsanity.com/paper/2301.10873/) (2023)
- [An Efficient Off-Policy Reinforcement Learning Algorithm for the Continuous-Time LQR Problem](https://mlsanity.com/paper/2303.17819/) (2023)
- [Data-Based Control of Continuous-Time Linear Systems with Performance Specifications](https://mlsanity.com/paper/2403.00424/) (2024)

## Abstract (arXiv)

This paper studies data-driven approaches to the continuous-time linear quadratic regulator (LQR) problem based on two existing parameterizations, namely a closed-loop (CL) parameterization from behavioral system theory and an integral reinforcement learning (IRL) parameterization. The CL parameterization characterizes the closed-loop system via a matrix that satisfies equality constraints. While this parameterization has been extensively studied for discrete-time systems, we adapt key results to the continuous-time setting and develop a policy iteration (PI) scheme, derive a data-driven continuous-time algebraic Riccati equation (CARE), and introduce an alternative convex problem formulation. The IRL parameterization utilizes off-policy data to perform policy evaluation, which is then used for PI or value iteration. Within the IRL framework, we derive a policy gradient flow and propose convex reformulations of the LQR problem. Finally, we provide a unified treatment of these parameterizations that enables a systematic understanding of existing approaches and clarifies their structural relationships.