mlsanityData to 14 Oct 2026

Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis

arXiv 2309.14648 ↗First posted 26 Sep 2023math.OC cs.LG math.STcited by 6

Not on the map. Why?

Abstract (arXiv)

This paper studies uncertainty set estimation for unknown linear systems. Uncertainty sets are crucial for the quality of robust control since they directly influence the conservativeness of the control design. Departing from the confidence region analysis of least squares estimation, this paper focuses on set membership estimation (SME). Though good numerical performances have attracted applications of SME in the control literature, the non-asymptotic convergence rate of SME for linear systems remains an open question. This paper provides the first convergence rate bounds for SME and discusses variations of SME under relaxed assumptions. We also provide numerical results demonstrating SME's practical promise.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 40 of its 85 references that are in the map. First posted on arXiv 26 Sep 2023.

Builds on

40 of 85 references.

References · 40

  1. 2021Convex optimizationcited by 2,515
  2. 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 371
  3. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 163
  4. 2017On the Sample Complexity of the Linear Quadratic Regulatorcited by 159
  5. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  6. 2020Naive Exploration is Optimal for Online LQRcited by 116
  7. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  8. 2018Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulatorcited by 86
  9. 2018Non-asymptotic Identification of LTI Systems from a Single Trajectorycited by 78
  10. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 53
  11. 2020Learning nonlinear dynamical systems from a single trajectorycited by 46
  12. 2020Black-Box Control for Linear Dynamical Systemscited by 43
28 more
  1. 2019Beyond Confidence Regions: Tight Bayesian Ambiguity Sets for Robust MDPscited by 40
  2. 2019Distributed Reinforcement Learning for Decentralized Linear Quadratic Control: A Derivative-Free Policy Optimization Approachcited by 38
  3. 2020Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectoriescited by 38
  4. 2018Safely Learning to Control the Constrained Linear Quadratic Regulatorcited by 33
  5. 2020Active Learning for Identification of Linear Dynamical Systemscited by 33
  6. 2021On the Regret Analysis of Online LQR Control with Predictionscited by 22
  7. 2020Reinforcement Learning with Fast Stabilization in Linear Dynamical Systemscited by 20
  8. 2020Online Optimal Control with Affine Constraintscited by 20
  9. 2017Thompson Sampling for Linear-Quadratic Control Problemscited by 14
  10. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12
  11. 2021Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guaranteescited by 11
  12. 2023Online switching control with stability and regret guaranteescited by 9
  13. 2019Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended versioncited by 8
  14. 2022Thompson Sampling Achieves tilde O(√T) Regret in Linear Quadratic Controlcited by 8
  15. 2022Robust adaptive MPC using control contraction metricscited by 8
  16. 2019Robust Adaptive Model Predictive Control: Performance and Parameter Estimationcited by 7
  17. 2020Set Membership identification of linear systems with guaranteed simulation accuracycited by 7
  18. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  19. 2022Augmented RBMLE-UCB Approach for Adaptive Control of Linear Quadratic Systemscited by 5
  20. 2022Online Adversarial Stabilization of Unknown Networked Systemscited by 5
  21. 2023Online Nonstochastic Control with Adversarial and Static Constraintscited by 5
  22. 2023Non-asymptotic System Identification for Linear Systems with Nonlinear Policiescited by 5
  23. 2023The informativity approach to data-driven analysis and controlcited by 4
  24. 2020Active exploration in adaptive model predictive controlcited by 3
  25. 2022Robust Online Voltage Control with an Unknown Grid Topologycited by 3
  26. 2019Robust Adaptive Model Predictive Control with Worst-Case Costcited by 2
  27. 2022Robust adaptive model predictive control with persistent excitation conditionscited by 2
  28. 2023When sampling works in data-driven control: Informativity for stabilization in continuous timecited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 3.

6 papers.

  1. 2024On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Setscited by 3
  2. 2025Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systemscited by 0
  3. 2025Frequency Response Identification of Low-Order Systems: Finite-Sample Analysiscited by 0
  4. 2026Online Learning for Supervisory Switching Controlcited by 0
  5. 2026Achieving widetildeO(1/ε) Sample Complexity for Bilinear Systems Identification under Bounded Noisescited by 0
  6. 2026Set Membership Estimation for Stochastic Linear Contextual Banditscited by 0