Data-Driven Continuous-Time Linear Quadratic Regulator via Closed-Loop and Reinforcement Learning Parameterizations
On the map: Deep reinforcement learning methods → RL for games and combinatorial optimization
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.
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.
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References · 16
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- 2019Formulas for Data-driven Control: Stabilization, Optimality and Robustnesscited by 47
- 2019Data informativity: a new perspective on data-driven analysis and controlcited by 19
- 2020Policy Gradient-based Algorithms for Continuous-time Linear Quadratic Controlcited by 13
- 2020From noisy data to feedback controllers: non-conservative design via a matrix S-lemmacited by 11
- 2024Data-Enabled Policy Optimization for Direct Adaptive Learning of the LQRcited by 9
- 2020Low-complexity Learning of Linear Quadratic Regulators from Noisy Datacited by 8
- 2019Robust data-driven state-feedback designcited by 7
- 2018Data-Driven LQR Control Designcited by 5
- 2021On the Certainty-Equivalence Approach to Direct Data-Driven LQR Designcited by 5
- 2025Regularization for Covariance Parameterization of Direct Data-Driven LQR Controlcited by 4
- 2021A Matrix Finsler's Lemma with Applications to Data-Driven Controlcited by 3
4 more
- 2023Data-enabled Policy Optimization for the Linear Quadratic Regulatorcited by 3
- 2023When sampling works in data-driven control: Informativity for stabilization in continuous timecited by 2
- 2023An Efficient Off-Policy Reinforcement Learning Algorithm for the Continuous-Time LQR Problemcited by 2
- 2024Data-Based Control of Continuous-Time Linear Systems with Performance Specificationscited by 1
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- 2025An Efficient Data-Driven Framework for Linear Quadratic Output Feedback Control ↗
- 2025Bridging Continuous-time LQR and Reinforcement Learning via Gradient Flow of the Bellman Error
- 2024Stability-Certified On-Policy Data-Driven LQR via Recursive Learning and Policy Gradient
- 2025A Fully Data-Driven Value Iteration for Stochastic LQR: Convergence, Robustness and Stability
- 2025Second-Order Policy Gradient Methods for the Linear Quadratic Regulator
- 2026Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems
- 2026Data-driven Linear Quadratic Integral Control: A Convex Formulation and Policy Gradient Approach ↗
- 2024MR-ARL: Model Reference Adaptive Reinforcement Learning for Robustly Stable On-Policy Data-Driven LQR