# Robust Policy Iteration for Continuous-time Linear Quadratic Regulation

arXiv: https://arxiv.org/abs/2005.09528 · HTML: https://mlsanity.com/paper/2005.09528/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2020.

## Built on by (most cited first, 15 of 15)

- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)
- [Reinforcement Learning for Adaptive Optimal Stationary Control of Linear Stochastic Systems](https://mlsanity.com/paper/2107.07788/) (2021)
- [Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies](https://mlsanity.com/paper/2210.04810/) (2022)
- [Inverse reinforcement learning by expert imitation for the stochastic linear-quadratic optimal control problem](https://mlsanity.com/paper/2405.17085/) (2024)
- [Robust Mean Field Social Control: A Unified Reinforcement Learning Framework](https://mlsanity.com/paper/2502.20029/) (2025)
- [Stability-Certified On-Policy Data-Driven LQR via Recursive Learning and Policy Gradient](https://mlsanity.com/paper/2403.05367/) (2024)
- [On the Robustness of Derivative-free Methods for Linear Quadratic Regulator](https://mlsanity.com/paper/2506.12596/) (2025)
- [Robust policy iteration for continuous-time stochastic H_∞ control problem with unknown dynamics](https://mlsanity.com/paper/2402.04721/) (2024)
- [MR-ARL: Model Reference Adaptive Reinforcement Learning for Robustly Stable On-Policy Data-Driven LQR](https://mlsanity.com/paper/2402.14483/) (2024)
- [Model-free H∞ control of Ito stochastic system via off-policy reinforcement learning](https://mlsanity.com/paper/2403.04412/) (2024)
- [Optimal Output Feedback Learning Control for Discrete-Time Linear Quadratic Regulation](https://mlsanity.com/paper/2503.06226/) (2025)
- [Some remarks on gradient dominance and LQR policy optimization](https://mlsanity.com/paper/2507.10452/) (2025)
- [Comparative Study of Q-Learning for State-Feedback LQG Control with an Unknown Model](https://mlsanity.com/paper/2511.07870/) (2025)
- [A Stochastic Gradient Descent Approach to Design Policy Gradient Methods for LQR](https://mlsanity.com/paper/2602.18933/) (2026)
- [Decentralized Strategies for Finite Population LQG Social Control: A Reinforcement Learning Approach](https://mlsanity.com/paper/2608.30244/) (2026)

## Abstract (arXiv)

This paper studies the robustness of policy iteration in the context of continuous-time infinite-horizon linear quadratic regulation (LQR) problem. It is shown that Kleinman's policy iteration algorithm is inherently robust to small disturbances and enjoys local input-to-state stability in the sense of Sontag. More precisely, whenever the disturbance-induced input term in each iteration is bounded and small, the solutions of the policy iteration algorithm are also bounded and enter a small neighborhood of the optimal solution of the LQR problem. Based on this result, an off-policy data-driven policy iteration algorithm for the LQR problem is shown to be robust when the system dynamics are subjected to small additive unknown bounded disturbances. The theoretical results are validated by a numerical example.