Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems

Chris Verhoek; Roland Tóth; Sofie Haesaert; Anne Koch

doi:10.1109/CDC45484.2021.9683151

Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

40 Citations (Scopus)

169 Downloads (Pure)

Abstract

Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential result for data-driven analysis and control. In this work, we aim to generalise this LTI result to Linear Parameter-Varying (LPV) systems. Based on the behavioural framework for LPV systems, we prove that one can obtain a result similar to Willems’. Based on an LPV representation, i.e., embedding, of nonlinear systems, this allows the application of the Fundamental Lemma for systems beyond the linear class.

Original language	English
Title of host publication	60th IEEE Conference on Decision and Control, CDC 2021
Publisher	Institute of Electrical and Electronics Engineers
Pages	5040-5046
Number of pages	7
ISBN (Electronic)	978-1-6654-3659-5
ISBN (Print)	978-1-6654-3660-1
DOIs	https://doi.org/10.1109/CDC45484.2021.9683151
Publication status	Published - 1 Feb 2022
Event	60th IEEE Conference on Decision and Control, CDC 2021 - Austin, TX, USA, Austin, United States Duration: 13 Dec 2021 → 17 Dec 2021 Conference number: 60 https://2021.ieeecdc.org/

Conference

Conference	60th IEEE Conference on Decision and Control, CDC 2021
Abbreviated title	CDC 2021
Country/Territory	United States
City	Austin
Period	13/12/21 → 17/12/21
Internet address	https://2021.ieeecdc.org/

Keywords

Behavioural System Theory
Data-Driven Analysis
Linear Parameter-Varying Systems

Access to Document

10.1109/CDC45484.2021.9683151

Author's versionFinal author version , 374 KBLicence: CC BY-NC

Cite this

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title = "Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems",

abstract = "Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential result for data-driven analysis and control. In this work, we aim to generalise this LTI result to Linear Parameter-Varying (LPV) systems. Based on the behavioural framework for LPV systems, we prove that one can obtain a result similar to Willems{\textquoteright}. Based on an LPV representation, i.e., embedding, of nonlinear systems, this allows the application of the Fundamental Lemma for systems beyond the linear class.",

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author = "Chris Verhoek and Roland T{\'o}th and Sofie Haesaert and Anne Koch",

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publisher = "Institute of Electrical and Electronics Engineers",

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note = "60th IEEE Conference on Decision and Control, CDC 2021, CDC 2021 ; Conference date: 13-12-2021 Through 17-12-2021",

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Verhoek, C , Tóth, R , Haesaert, S & Koch, A 2022, Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems. in 60th IEEE Conference on Decision and Control, CDC 2021., 9683151, Institute of Electrical and Electronics Engineers, pp. 5040-5046, 60th IEEE Conference on Decision and Control, CDC 2021, Austin, Texas, United States, 13/12/21. https://doi.org/10.1109/CDC45484.2021.9683151

Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems. / Verhoek, Chris ; Tóth, Roland ; Haesaert, Sofie et al.
60th IEEE Conference on Decision and Control, CDC 2021. Institute of Electrical and Electronics Engineers, 2022. p. 5040-5046 9683151.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems

AU - Verhoek, Chris

AU - Tóth, Roland

AU - Haesaert, Sofie

AU - Koch, Anne

N1 - Conference code: 60

PY - 2022/2/1

Y1 - 2022/2/1

N2 - Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential result for data-driven analysis and control. In this work, we aim to generalise this LTI result to Linear Parameter-Varying (LPV) systems. Based on the behavioural framework for LPV systems, we prove that one can obtain a result similar to Willems’. Based on an LPV representation, i.e., embedding, of nonlinear systems, this allows the application of the Fundamental Lemma for systems beyond the linear class.

AB - Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential result for data-driven analysis and control. In this work, we aim to generalise this LTI result to Linear Parameter-Varying (LPV) systems. Based on the behavioural framework for LPV systems, we prove that one can obtain a result similar to Willems’. Based on an LPV representation, i.e., embedding, of nonlinear systems, this allows the application of the Fundamental Lemma for systems beyond the linear class.

KW - Behavioural System Theory

KW - Data-Driven Analysis

KW - Linear Parameter-Varying Systems

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M3 - Conference contribution

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BT - 60th IEEE Conference on Decision and Control, CDC 2021

PB - Institute of Electrical and Electronics Engineers

T2 - 60th IEEE Conference on Decision and Control, CDC 2021

Y2 - 13 December 2021 through 17 December 2021

ER -

Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems

Abstract

Conference

Keywords

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