mlsanityData to 7 Oct 2026

Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectories

arXiv 2009.00739 ↗First posted 1 Sep 2020math.OC cs.SY eess.SYcited by 38

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Abstract (arXiv)

This paper considers the problem of linear time-invariant (LTI) system identification using input/output data. Recent work has provided non-asymptotic results on partially observed LTI system identification using a single trajectory but is only suitable for stable systems. We provide finite-time analysis for learning Markov parameters based on the ordinary least-squares (OLS) estimator using multiple trajectories, which covers both stable and unstable systems. For unstable systems, our results suggest that the Markov parameters are harder to estimate in the presence of process noise. Without process noise, our upper bound on the estimation error is independent of the spectral radius of system dynamics with high probability. These two features are different from fully observed LTI systems for which recent work has shown that unstable systems with a bigger spectral radius are easier to estimate. Extensive numerical experiments demonstrate the performance of our OLS estimator.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Sep 2020.

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Citing papers per year: 2021: 6; 2022: 9; 2023: 5; 2024: 11; 2025: 5; 2026: 2.

38 papers.

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  1. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 52
  2. 2023A New Approach to Learning Linear Dynamical Systemscited by 23
  3. 2021Linear Systems can be Hard to Learncited by 20
  4. 2022Identifying the Dynamics of a System by Leveraging Data from Similar Systemscited by 15
  5. 2022FedSysID: A Federated Approach to Sample-Efficient System Identificationcited by 15
  6. 2022Learning to Control Linear Systems can be Hardcited by 10
  7. 2023Learning Personalized Models with Clustered System Identificationcited by 10
  8. 2022Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectoriescited by 8
  9. 2023Learning Dynamical Systems by Leveraging Data from Similar Systemscited by 8
  10. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  11. 2024Outlier-Robust Linear System Identification Under Heavy-tailed Noisecited by 4
  12. 2021Online Stochastic Gradient Descent Learns Linear Dynamical Systems from A Single Trajectorycited by 3
26 more
  1. 2022Distributed Online System Identification for LTI Systems Using Reverse Experience Replaycited by 3
  2. 2023Learning Linearized Models from Nonlinear Systems with Finite Datacited by 3
  3. 2021Large-Scale System Identification Using a Randomized SVDcited by 2
  4. 2024Learning Low-dimensional Latent Dynamics from High-dimensional Observations: Non-asymptotics and Lower Boundscited by 2
  5. 2024Length independent generalization bounds for deep SSM architectures via Rademacher contraction and stability constraintscited by 2
  6. 2024Learning to Stabilize Unknown LTI Systems on a Single Trajectory under Stochastic Noisecited by 2
  7. 2024Combining Federated Learning and Control: A Surveycited by 2
  8. 2025Model-free Online Learning for the Kalman Filter: Forgetting Factor and Logarithmic Regretcited by 2
  9. 2021OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regressioncited by 1
  10. 2022Learning Transition Operators From Sparse Space-Time Samplescited by 1
  11. 2022Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identificationcited by 1
  12. 2024Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systemscited by 1
  13. 2025Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Datacited by 1
  14. 2025Logarithmic Regret and Polynomial Scaling in Online Multi-step-ahead Predictioncited by 1
  15. 2021Safe Linear-Quadratic Dual Control with Almost Sure Performance Guaranteecited by 0
  16. 2021Learning Linear Models Using Distributed Iterative Hessian Sketchingcited by 0
  17. 2022System Identification via Nuclear Norm Regularizationcited by 0
  18. 2024A finite-sample generalization bound for stable LPV systemscited by 0
  19. 2024Joint Learning of Linear Dynamical Systems under Smoothness Constraintscited by 0
  20. 2024Learning Dynamic Bayesian Networks from Data: Foundations, First Principles and Numerical Comparisonscited by 0
  21. 2024Finite Sample Analysis of Distribution-Free Confidence Ellipsoids for Linear Regressioncited by 0
  22. 2024On the Effect of Instability on Learning Continuous-Time Linear Control Systemscited by 0
  23. 2025Boosting-Enabled Robust System Identification of Partially Observed LTI Systems Under Heavy-Tailed Noisecited by 0
  24. 2025Frequency Response Identification of Low-Order Systems: Finite-Sample Analysiscited by 0
  25. 2026Symplectic Inductive Bias for Data-Driven Target Reachability in Hamiltonian Systemscited by 0
  26. 2026Learning Fractional-Order Dynamics from a Single Trajectorycited by 0