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Non-asymptotic Identification of LTI Systems from a Single Trajectory

arXiv 1806.05722 ↗First posted 14 Jun 2018cs.LG cs.SY eess.SYcited by 77

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Abstract (arXiv)

We consider the problem of learning a realization for a linear time-invariant (LTI) dynamical system from input/output data. Given a single input/output trajectory, we provide finite time analysis for learning the system's Markov parameters, from which a balanced realization is obtained using the classical Ho-Kalman algorithm. By proving a stability result for the Ho-Kalman algorithm and combining it with the sample complexity results for Markov parameters, we show how much data is needed to learn a balanced realization of the system up to a desired accuracy with high probability.

Key facts. Cited by 77 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Jun 2018.

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Citing papers per year: 2021: 19; 2022: 17; 2023: 15; 2024: 10; 2025: 8; 2026: 8.

77 papers.

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  1. 2022Provable Reinforcement Learning with a Short-Term Memorycited by 40
  2. 2024From Self-Attention to Markov Models: Unveiling the Dynamics of Generative Transformerscited by 34
  3. 2022Single Trajectory Nonparametric Learning of Nonlinear Dynamicscited by 26
  4. 2023A Tutorial on the Non-Asymptotic Theory of System Identificationcited by 26
  5. 2023A New Approach to Learning Linear Dynamical Systemscited by 23
  6. 2021Linear Systems can be Hard to Learncited by 20
  7. 2021Streaming Linear System Identification with Reverse Experience Replaycited by 17
  8. 2021Task-Optimal Exploration in Linear Dynamical Systemscited by 15
  9. 2022Learning Mixtures of Linear Dynamical Systemscited by 15
  10. 2022Identifying the Dynamics of a System by Leveraging Data from Similar Systemscited by 15
  11. 2022FedSysID: A Federated Approach to Sample-Efficient System Identificationcited by 15
  12. 2021Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Boundscited by 13
38 more
  1. 2022Online Control of Unknown Time-Varying Dynamical Systemscited by 13
  2. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12
  3. 2022Learning to Control Linear Systems can be Hardcited by 10
  4. 2023Learning Personalized Models with Clustered System Identificationcited by 10
  5. 2023Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systemscited by 10
  6. 2021Learning from Censored and Dependent Data: The case of Linear Dynamicscited by 9
  7. 2022Provable Sim-to-real Transfer in Continuous Domain with Partial Observationscited by 9
  8. 2023Smoothed Online Learning for Prediction in Piecewise Affine Systemscited by 9
  9. 2023An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysiscited by 9
  10. 2024Model Stealing for Any Low-Rank Language Modelcited by 9
  11. 2022Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectoriescited by 8
  12. 2023Learning Dynamical Systems by Leveraging Data from Similar Systemscited by 8
  13. 2023Physics-Regulated Deep Reinforcement Learning: Invariant Embeddingscited by 8
  14. 2021PAC-Bayesian theory for stochastic LTI systemscited by 6
  15. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  16. 2021Deep inference of latent dynamics with spatio-temporal super-resolution using selective backpropagation through timecited by 6
  17. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  18. 2024Learning Linear Dynamics from Bilinear Observationscited by 6
  19. 2023Oracle-Efficient Smoothed Online Learning for Piecewise Continuous Decision Makingcited by 5
  20. 2023Non-asymptotic System Identification for Linear Systems with Nonlinear Policiescited by 5
  21. 2025Universal Learning of Nonlinear Dynamicscited by 5
  22. 2021Robust Online Control with Model Misspecificationcited by 4
  23. 2021Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systemscited by 4
  24. 2021Strong Consistency and Rate of Convergence of Switched Least Squares System Identification for Autonomous Markov Jump Linear Systemscited by 4
  25. 2023Non-Asymptotic Pointwise and Worst-Case Bounds for Classical Spectrum Estimatorscited by 4
  26. 2024Outlier-Robust Linear System Identification Under Heavy-tailed Noisecited by 4
  27. 2021Online Stochastic Gradient Descent Learns Linear Dynamical Systems from A Single Trajectorycited by 3
  28. 2021Certainty Equivalent Quadratic Control for Markov Jump Systemscited by 3
  29. 2021Online Learning for Predictive Control with Provable Regret Guaranteescited by 3
  30. 2022Distributed Online System Identification for LTI Systems Using Reverse Experience Replaycited by 3
  31. 2022Dynamical Linear Banditscited by 3
  32. 2022Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part Icited by 3
  33. 2023PAC-Bayesian bounds for learning LTI-ss systems with input from empirical losscited by 3
  34. 2023Learning Linearized Models from Nonlinear Systems with Finite Datacited by 3
  35. 2021Algorithms from Invariants: Smoothed Analysis of Orbit Recovery over SO(3)cited by 2
  36. 2021Large-Scale System Identification Using a Randomized SVDcited by 2
  37. 2024Learning Low-dimensional Latent Dynamics from High-dimensional Observations: Non-asymptotics and Lower Boundscited by 2
  38. 2024Learning to Stabilize Unknown LTI Systems on a Single Trajectory under Stochastic Noisecited by 2

50 most cited of 77 All 77 (JSON)