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

Bruce Lee; Andrew Lamperski

doi:10.1109/CDC42340.2020.9304468

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

Bruce Lee, Andrew Lamperski

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

15 Scopus citations

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 language	English (US)
Title of host publication	2020 59th IEEE Conference on Decision and Control, CDC 2020
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3419-3424
Number of pages	6
ISBN (Electronic)	9781728174471
DOIs	https://doi.org/10.1109/CDC42340.2020.9304468
State	Published - Dec 14 2020
Externally published	Yes
Event	59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of Duration: Dec 14 2020 → Dec 18 2020

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2020-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	59th IEEE Conference on Decision and Control, CDC 2020
Country/Territory	Korea, Republic of
City	Virtual, Jeju Island
Period	12/14/20 → 12/18/20

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.

Access

10.1109/CDC42340.2020.9304468

OpenUrl availability

Full text

Cite this

Lee, B., & Lamperski, A. (2020). Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction. In 2020 59th IEEE Conference on Decision and Control, CDC 2020 (pp. 3419-3424). Article 9304468 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC42340.2020.9304468

Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction. / Lee, Bruce; Lamperski, Andrew.
2020 59th IEEE Conference on Decision and Control, CDC 2020. Institute of Electrical and Electronics Engineers Inc., 2020. p. 3419-3424 9304468 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Lee, B & Lamperski, A 2020, Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction. in 2020 59th IEEE Conference on Decision and Control, CDC 2020., 9304468, Proceedings of the IEEE Conference on Decision and Control, vol. 2020-December, Institute of Electrical and Electronics Engineers Inc., pp. 3419-3424, 59th IEEE Conference on Decision and Control, CDC 2020, Virtual, Jeju Island, Korea, Republic of, 12/14/20. https://doi.org/10.1109/CDC42340.2020.9304468

Lee B, Lamperski A. Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction. In 2020 59th IEEE Conference on Decision and Control, CDC 2020. Institute of Electrical and Electronics Engineers Inc. 2020. p. 3419-3424. 9304468. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC42340.2020.9304468

@inproceedings{bb09dbfe2adf4d4a87efb7cb0668744a,

title = "Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction",

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.",

author = "Bruce Lee and Andrew Lamperski",

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: {\textcopyright} 2020 IEEE.; 59th IEEE Conference on Decision and Control, CDC 2020 ; Conference date: 14-12-2020 Through 18-12-2020",

year = "2020",

month = dec,

day = "14",

doi = "10.1109/CDC42340.2020.9304468",

language = "English (US)",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "3419--3424",

booktitle = "2020 59th IEEE Conference on Decision and Control, CDC 2020",

}

TY - GEN

T1 - Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction

AU - Lee, Bruce

AU - Lamperski, Andrew

N1 - 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.

PY - 2020/12/14

Y1 - 2020/12/14

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85099881444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85099881444&partnerID=8YFLogxK

U2 - 10.1109/CDC42340.2020.9304468

DO - 10.1109/CDC42340.2020.9304468

M3 - Conference contribution

AN - SCOPUS:85099881444

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3419

EP - 3424

BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 59th IEEE Conference on Decision and Control, CDC 2020

Y2 - 14 December 2020 through 18 December 2020

ER -

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

Abstract

Publication series

Conference

Bibliographical note

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this