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

TL;DR

This paper offers a non-asymptotic analysis of closed-loop system identification using autoregressive models and Hankel model reduction, providing bounds on model accuracy and error with finite data.

Contribution

It introduces the first non-asymptotic bounds for a specific autoregressive and Hankel model reduction algorithm in closed-loop system identification.

Findings

Provides upper bounds on generalization error.

Establishes high probability bounds on model deviation from the finite horizon Kalman Filter.

Addresses bias issues in closed-loop data identification.

Abstract

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.