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

Bruce Lee, Andrew Lamperski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 to eliminate these biases involves first fitting a long-horizon autoregressive model and 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.

Original languageEnglish (US)
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3419-3424
Number of pages6
ISBN (Electronic)9781728174471
DOIs
StatePublished - Dec 14 2020
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: Dec 14 2020Dec 18 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2020-December
ISSN (Print)0743-1546

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
CountryKorea, Republic of
CityVirtual, Jeju Island
Period12/14/2012/18/20

Bibliographical note

Funding Information:
This work was supported in part by NSF CMMI-1727096 B.L. is a graduate student at the University of Pennsylvania A.L. is with the department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA

Publisher Copyright:
© 2020 IEEE.

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