mlsanityData to 14 Oct 2026

Active Learning for Identification of Linear Dynamical Systems

arXiv 2002.00495 ↗First posted 2 Feb 2020cs.LG cs.SY eess.SYcited by 33

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Abstract (arXiv)

We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound quantifying the estimation rate our algorithm attains and prove matching upper and lower bounds which guarantee its asymptotic optimality, up to constants. In addition, we show that this optimal rate is unattainable when using Gaussian noise to excite the system, even with optimally tuned covariance, and analyze several examples where our algorithm provably improves over rates obtained by playing noise. Our analysis critically relies on a novel result quantifying the error in estimating the parameters of a dynamical system when arbitrary periodic inputs are being played. We conclude with numerical examples that illustrate the effectiveness of our algorithm in practice.

Key facts. Cited by 33 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 Feb 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 5; 2022: 5; 2023: 7; 2024: 7; 2025: 3; 2026: 6.

33 papers.

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  1. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 53
  2. 2023Optimistic Active Exploration of Dynamical Systemscited by 32
  3. 2024ASID: Active Exploration for System Identification in Robotic Manipulationcited by 28
  4. 2023A Tutorial on the Non-Asymptotic Theory of System Identificationcited by 26
  5. 2021Linear Systems can be Hard to Learncited by 20
  6. 2023Optimal Exploration for Model-Based RL in Nonlinear Systemscited by 18
  7. 2021Task-Optimal Exploration in Linear Dynamical Systemscited by 15
  8. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12
  9. 2022Learning to Control Linear Systems can be Hardcited by 11
  10. 2023Learning Dynamical Systems by Leveraging Data from Similar Systemscited by 8
  11. 2024Active Learning for Control-Oriented Identification of Nonlinear Systemscited by 7
  12. 2026LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Searchcited by 7
21 more
  1. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  2. 2024Learning Linear Dynamics from Bilinear Observationscited by 6
  3. 2025Finite Sample Identification of Partially Observed Bilinear Dynamical Systemscited by 5
  4. 2021Time varying regression with hidden linear dynamicscited by 4
  5. 2021Online Stochastic Gradient Descent Learns Linear Dynamical Systems from A Single Trajectorycited by 3
  6. 2024Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketchingcited by 3
  7. 2023Exact Recovery for System Identification with More Corrupt Data than Clean Datacited by 2
  8. 2022Online greedy identification of linear dynamical systemscited by 1
  9. 2023Deep active learning for nonlinear system identificationcited by 1
  10. 2024Finite Sample Frequency Domain Identificationcited by 1
  11. 2024Active learning of neural population dynamics using two-photon holographic optogeneticscited by 1
  12. 2025Optimal Bayesian Affine Estimator and Active Learning for the Wiener Modelcited by 1
  13. 2025High Effort, Low Gain: Fundamental Limits of Active Learning for Linear Dynamical Systemscited by 1
  14. 2021Safe Linear-Quadratic Dual Control with Almost Sure Performance Guaranteecited by 0
  15. 2022System Identification via Nuclear Norm Regularizationcited by 0
  16. 2024Active Learning of Dynamics Using Prior Domain Knowledge in the Sampling Processcited by 0
  17. 2026Optimal Centered Active Excitation in Linear System Identificationcited by 0
  18. 2026A Memory Efficient Unified Algorithm for Online Learning of Linear Dynamical Systemscited by 0
  19. 2026Trajectory Design and Budgeted Querying for Digital Twin Calibrationcited by 0
  20. 2026Target-Independent Micro-Interventions for Predicting Training Response Across Language-Model Familiescited by 0
  21. 2026ALDER: Discovering the Laws of a World by Acting in Itcited by 0