# Safely Learning to Control the Constrained Linear Quadratic Regulator

arXiv: https://arxiv.org/abs/1809.10121 · HTML: https://mlsanity.com/paper/1809.10121/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2018.

## Built on by (most cited first, 30 of 33)

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- [Safe Autonomous Racing via Approximate Reachability on Ego-vision](https://mlsanity.com/paper/2110.07699/) (2021)
- [Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees](https://mlsanity.com/paper/2111.00411/) (2021)
- [Learning Dynamical Systems by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2302.04344/) (2023)
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- [Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraints](https://mlsanity.com/paper/2209.07040/) (2022)
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- [Adaptive Robust Model Predictive Control via Uncertainty Cancellation](https://mlsanity.com/paper/2212.01371/) (2022)
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- [Exact Recovery Guarantees for Parameterized Nonlinear System Identification Problem under Sparse Disturbances or Semi-Oblivious Attacks](https://mlsanity.com/paper/2409.00276/) (2024)
- [Learning Safety Filters for Unknown Discrete-Time Linear Systems](https://mlsanity.com/paper/2111.00631/) (2021)
- [System Identification via Nuclear Norm Regularization](https://mlsanity.com/paper/2203.16673/) (2022)
- [Learning Nonlinear Couplings in Network of Agents from a Single Sample Trajectory](https://mlsanity.com/paper/2211.11069/) (2022)
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- [Finite Time Regret Bounds for Minimum Variance Control of Autoregressive Systems with Exogenous Inputs](https://mlsanity.com/paper/2305.16974/) (2023)
- [Learning to Stabilize Online Reinforcement Learning in Unbounded State Spaces](https://mlsanity.com/paper/2306.01896/) (2023)

## Abstract (arXiv)

We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of state and input constraints. This framework involves a novel method for synthesizing robust constraint-satisfying feedback controllers, leveraging newly developed tools from system level synthesis. We connect statistical results with cost sub-optimality bounds to give non-asymptotic guarantees on both estimation and controller performance.