mlsanityData to 14 Oct 2026

Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis

arXiv 2508.17142 ↗First posted 23 Aug 2025eess.SY cs.LG cs.SYcited by 0

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Abstract (arXiv)

This paper proposes a frequency-domain estimator for low-order systems from repeated noisy measurements. The estimator minimizes a quadratic data-fitting term regularized by the nuclear norm of a Loewner matrix, subject to a convex stability constraint enforced via a semidefinite program. We prove a finite-sample error bound at the sampled frequencies and extend it to all frequencies through rational interpolation. The bound characterizes the dependence on the number of repeated experiments, number of frequency points, system order, and noise level. Numerical experiments on SISO and MIMO systems demonstrate the low-order-promoting effect of the method and validate the predicted scaling laws.

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References · 32

  1. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
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  4. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
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20 more
  1. 2019Sample Complexity Lower Bounds for Linear System Identificationcited by 20
  2. 2020Improved rates for prediction and identification of partially observed linear dynamical systemscited by 12
  3. 2015Regularized linear system identification using atomic, nuclear and kernel-based norms: the role of the stability constraintcited by 11
  4. 2019Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolationcited by 6
  5. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  6. 2015Robust recovery of complex exponential signals from random Gaussian projections via low rank Hankel matrix reconstructioncited by 5
  7. 2025Finite Sample Identification of Partially Observed Bilinear Dynamical Systemscited by 5
  8. 2025Generalization Error Analysis for Selective State-Space Models Through the Lens of Attentioncited by 5
  9. 2023Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regressioncited by 4
  10. 2024Online Optimization Perspective on First-Order and Zero-Order Decentralized Nonsmooth Nonconvex Stochastic Optimizationcited by 4
  11. 2024Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems with Neural Network Controllerscited by 4
  12. 2024Outlier-Robust Linear System Identification Under Heavy-tailed Noisecited by 4
  13. 2024Sample Complexity Bounds for Linear System Identification from a Finite Setcited by 3
  14. 2024Convex Data-Driven Contraction With Riemannian Metricscited by 3
  15. 2022Frequency Domain Gaussian Process Models for H^∞ Uncertaintiescited by 2
  16. 2025Safe Control for Pursuit-Evasion with Density Functionscited by 2
  17. 2025Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraintscited by 2
  18. 2023Frequency-Domain Identification of Discrete-Time Systems using Sum-of-Rational Optimizationcited by 1
  19. 2024Finite Sample Frequency Domain Identificationcited by 1
  20. 2024Quantile Fourier regressions for decision making under uncertaintycited by 1

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