# Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction

arXiv: https://arxiv.org/abs/1909.02192 · HTML: https://mlsanity.com/paper/1909.02192/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2019.

## Built on by (most cited first, 9 of 9)

- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [A Tutorial on the Non-Asymptotic Theory of System Identification](https://mlsanity.com/paper/2309.03873/) (2023)
- [A New Approach to Learning Linear Dynamical Systems](https://mlsanity.com/paper/2301.09519/) (2023)
- [Linear Systems can be Hard to Learn](https://mlsanity.com/paper/2104.01120/) (2021)
- [Streaming Linear System Identification with Reverse Experience Replay](https://mlsanity.com/paper/2103.05896/) (2021)
- [Learning to Control Linear Systems can be Hard](https://mlsanity.com/paper/2205.14035/) (2022)
- [Non-Asymptotic Pointwise and Worst-Case Bounds for Classical Spectrum Estimators](https://mlsanity.com/paper/2303.11908/) (2023)
- [Learning Linear Models Using Distributed Iterative Hessian Sketching](https://mlsanity.com/paper/2112.04101/) (2021)
- [Two-Layer Linear Auto-Regressive Models Estimate Latent States](https://mlsanity.com/paper/2606.12691/) (2026)

## Abstract (arXiv)

One of the primary challenges of system identification is determining how much data is necessary to adequately fit a model. Non-asymptotic characterizations of the performance of system identification methods provide this knowledge. Such characterizations are available for several algorithms performing open-loop identification. Often times, however, data is collected in closed-loop. Application of open-loop identification methods to closed-loop data can result in biased estimates. One method used by subspace identification techniques to eliminate these biases involves first fitting a long-horizon autoregressive model, then performing model reduction. The asymptotic behavior of such algorithms is well characterized, but the non-asymptotic behavior is not. This work provides a non-asymptotic characterization of one particular variant of these algorithms. More specifically, we provide non-asymptotic upper bounds on the generalization error of the produced model, as well as high probability bounds on the difference between the produced model and the finite horizon Kalman Filter.