Data-Driven Tests for Controllability

Vikas Kumar Mishra; Ivan Markovsky; Ben Grossmann

doi:10.1109/LCSYS.2020.3003770

Data-Driven Tests for Controllability

Vikas Kumar Mishra, Ivan Markovsky, Ben Grossmann

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

The fundamental lemma due to Willems et al. 'A note on persistency of excitation,' Syst. Control Lett., vol. 54, no. 4, pp. 325-329, 2005 plays an important role in system identification and data-driven control. One of the assumptions for the fundamental lemma is that the underlying linear time-invariant system is controllable. In this letter, the fundamental lemma is extended to address system identification for uncontrollable systems. Then, a data-driven algebraic test is derived to check whether the underlying system is controllable or not. An algorithm based on the singular value decomposition of a Hankel matrix constructed from the data is provided to implement the developed test. The algorithm has cubic computational cost. Examples are given to illustrate the theoretical results.

Original language	English
Article number	9121339
Pages (from-to)	517-522
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	5
Issue number	2
DOIs	https://doi.org/10.1109/LCSYS.2020.3003770
State	Published - 1 Apr 2021
Externally published	Yes

Keywords

Behavioral approach
data-driven controllability
system identification

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization

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10.1109/LCSYS.2020.3003770

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abstract = "The fundamental lemma due to Willems et al. 'A note on persistency of excitation,' Syst. Control Lett., vol. 54, no. 4, pp. 325-329, 2005 plays an important role in system identification and data-driven control. One of the assumptions for the fundamental lemma is that the underlying linear time-invariant system is controllable. In this letter, the fundamental lemma is extended to address system identification for uncontrollable systems. Then, a data-driven algebraic test is derived to check whether the underlying system is controllable or not. An algorithm based on the singular value decomposition of a Hankel matrix constructed from the data is provided to implement the developed test. The algorithm has cubic computational cost. Examples are given to illustrate the theoretical results.",

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AB - The fundamental lemma due to Willems et al. 'A note on persistency of excitation,' Syst. Control Lett., vol. 54, no. 4, pp. 325-329, 2005 plays an important role in system identification and data-driven control. One of the assumptions for the fundamental lemma is that the underlying linear time-invariant system is controllable. In this letter, the fundamental lemma is extended to address system identification for uncontrollable systems. Then, a data-driven algebraic test is derived to check whether the underlying system is controllable or not. An algorithm based on the singular value decomposition of a Hankel matrix constructed from the data is provided to implement the developed test. The algorithm has cubic computational cost. Examples are given to illustrate the theoretical results.

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Data-Driven Tests for Controllability

Abstract

Keywords

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