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Achieving widetildeO(1/ε) Sample Complexity for Bilinear Systems Identification under Bounded Noises

arXiv 2603.20819 ↗First posted 21 Mar 2026cs.LG cs.SY eess.SYcited by 0

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Abstract (arXiv)

This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Our analysis considers trajectory-dependent regressors and allows marginally stable dynamics with polynomial mean-square state growth. We prove that the diameter of the feasible parameter set shrinks with sample complexity widetildemathcal O(1/ε) where ε is the estimation error. Simulation supports the theory and illustrates the advantage of the proposed estimator for uncertainty quantification.

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References · 15

  1. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  2. 2020Naive Exploration is Optimal for Online LQRcited by 116
  3. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  4. 2018Non-asymptotic Identification of LTI Systems from a Single Trajectorycited by 78
  5. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12
  6. 2020Set Membership identification of linear systems with guaranteed simulation accuracycited by 7
  7. 2024Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guaranteescited by 7
  8. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  9. 2024CLOSURE: Fast Quantification of Pose Uncertainty Setscited by 6
  10. 2022Online Adversarial Stabilization of Unknown Networked Systemscited by 5
  11. 2025Finite Sample Identification of Partially Observed Bilinear Dynamical Systemscited by 5
  12. 2024On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Setscited by 3
3 more
  1. 2025System Identification Under Bounded Noise: Optimal Rates Beyond Least Squarescited by 2
  2. 2022Dual adaptive MPC using an exact set-membership reformulationcited by 1
  3. 2025A finite-sample bound for identifying partially observed linear switched systems from a single trajectorycited by 1

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