A Matrix Finsler’s Lemma with Applications to Data-Driven Control

Henk van Waarde; Kanat Camlibel

doi:10.1109/CDC45484.2021.9683285

A Matrix Finsler’s Lemma with Applications to Data-Driven Control

Henk van Waarde, Kanat Camlibel^*

^*Corresponding author for this work

Systems, Control and Applied Analysis

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

7 Citations (Scopus)

72 Downloads (Pure)

Abstract

In a recent paper it was shown how a matrix S-lemma can be applied to construct controllers from noisy data. The current paper complements these results by proving a matrix version of the classical Finsler's lemma. This matrix Finsler's lemma provides a tractable condition under which all matrix solutions to a quadratic equality also satisfy a quadratic inequality. We will apply this result to bridge known data- driven control design techniques for both exact and noisy data, thereby revealing a more general theory. The result is also applied to data-driven control of Lur'e systems.

Original language	English
Title of host publication	The 60 IEEE Conference on Decision and Control
Subtitle of host publication	Proceedings
Publisher	IEEE
Pages	5777-5782
Number of pages	6
DOIs	https://doi.org/10.1109/CDC45484.2021.9683285
Publication status	Published - 1-Feb-2022
Event	The 60th IEEE conference on Decision and Control (CDC 2021) - Austin, Texas, United States Duration: 13-Dec-2021 → 17-Dec-2021

Conference

Conference	The 60th IEEE conference on Decision and Control (CDC 2021)
Country/Territory	United States
City	Austin, Texas
Period	13/12/2021 → 17/12/2021

Access to Document

10.1109/CDC45484.2021.9683285

A Matrix Finsler’s Lemma with Applications to Data-Driven ControlFinal publisher's version, 934 KBLicence: Taverne

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Cite this

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abstract = "In a recent paper it was shown how a matrix S-lemma can be applied to construct controllers from noisy data. The current paper complements these results by proving a matrix version of the classical Finsler's lemma. This matrix Finsler's lemma provides a tractable condition under which all matrix solutions to a quadratic equality also satisfy a quadratic inequality. We will apply this result to bridge known data- driven control design techniques for both exact and noisy data, thereby revealing a more general theory. The result is also applied to data-driven control of Lur'e systems.",

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AB - In a recent paper it was shown how a matrix S-lemma can be applied to construct controllers from noisy data. The current paper complements these results by proving a matrix version of the classical Finsler's lemma. This matrix Finsler's lemma provides a tractable condition under which all matrix solutions to a quadratic equality also satisfy a quadratic inequality. We will apply this result to bridge known data- driven control design techniques for both exact and noisy data, thereby revealing a more general theory. The result is also applied to data-driven control of Lur'e systems.

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