mlsanityData to 7 Oct 2026

Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees

arXiv 2111.00411 ↗First posted 31 Oct 2021eess.SY cs.LG cs.SYcited by 10

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Abstract (arXiv)

We study the adaptive control of an unknown linear system with a quadratic cost function subject to safety constraints on both the states and actions. The challenges of this problem arise from the tension among safety, exploration, performance, and computation. To address these challenges, we propose a polynomial-time algorithm that guarantees feasibility and constraint satisfaction with high probability under proper conditions. Our algorithm is implemented on a single trajectory and does not require system restarts. Further, we analyze the regret of our learning algorithm compared to the optimal safe linear controller with known model information. The proposed algorithm can achieve a tilde O(T2/3) regret, where T is the number of stages and tilde O(·) absorbs some logarithmic terms of T.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 23 of its 56 references that are in the map. First posted on arXiv 31 Oct 2021.

Builds on

23 of 56 references.

References · 23

  1. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 261
  2. 2019End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Taskscited by 256
  3. 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 211
  4. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  5. 2017On the Sample Complexity of the Linear Quadratic Regulatorcited by 151
  6. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 150
  7. 2013Risk-sensitive Reinforcement Learningcited by 129
  8. 2020Naive Exploration is Optimal for Online LQRcited by 111
  9. 2019Online Control with Adversarial Disturbancescited by 92
  10. 2018Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulatorcited by 86
  11. 2020Improper Learning for Non-Stochastic Controlcited by 83
  12. 2020Learning nonlinear dynamical systems from a single trajectorycited by 46
11 more
  1. 2020Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systemscited by 39
  2. 2019Logarithmic Regret for Online Controlcited by 38
  3. 2018Linear model predictive safety certification for learning-based controlcited by 34
  4. 2018Safely Learning to Control the Constrained Linear Quadratic Regulatorcited by 31
  5. 2020Online Optimal Control with Affine Constraintscited by 20
  6. 2019LMI Properties and Applications in Systems, Stability, and Control Theorycited by 11
  7. 2020Geometric Exploration for Online Controlcited by 9
  8. 2019Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended versioncited by 8
  9. 2019Robust Adaptive Model Predictive Control: Performance and Parameter Estimationcited by 7
  10. 2019Adaptive MPC under Time Varying Uncertainty: Robust and Stochasticcited by 6
  11. 2019Adaptive Model Predictive Control for A Class of Constrained Linear Systems with Parametric Uncertaintiescited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 3; 2023: 5; 2024: 0; 2025: 0; 2026: 1.

10 papers.

  1. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  2. 2023Non-asymptotic System Identification for Linear Systems with Nonlinear Policiescited by 5
  3. 2022Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraintscited by 3
  4. 2023Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraintscited by 2
  5. 2023Exact Recovery for System Identification with More Corrupt Data than Clean Datacited by 2
  6. 2022Learning Decentralized Linear Quadratic Regulators with √T Regretcited by 1
  7. 2023Anytime-Competitive Reinforcement Learning with Policy Priorcited by 1
  8. 2021Learning Safety Filters for Unknown Discrete-Time Linear Systemscited by 0
  9. 2022Rate-matching the regret lower-bound in the linear quadratic regulator with unknown dynamicscited by 0
  10. 2026When Can Safe Controllers Adapt? Information before Commitmentcited by 0