TY - JOUR
T1 - Data-Driven Tests for Controllability
AU - Mishra, Vikas Kumar
AU - Markovsky, Ivan
AU - Grossmann, Ben
N1 - Funding Information:
Manuscript received March 13, 2020; revised May 22, 2020; accepted June 6, 2020. Date of publication June 19, 2020; date of current version July 3, 2020. This work was supported in part by the Fond for Scientific Research Vlaanderen (FWO) Project under Grant G090117N “Block-Oriented Nonlinear Identification Using Volterra Series,” and in part by the FNRS–FWO Vlaanderen under Excellence of Science Project under Grant 30468160 “Structured Low-Rank Matrix/Tensor Approximation: Numerical Optimization-Based Algorithms and Applications.” Recommended by Senior Editor R. S. Smith. (Corresponding author: Vikas Kumar Mishra.) The authors are with the Department ELEC, Vrije Universiteit Brussel, 1050 Brussels, Belgium (e-mail: vmishra@vub.be; imarkovs@vub.be; bgrossma@vub.be). Digital Object Identifier 10.1109/LCSYS.2020.3003770
Publisher Copyright:
© 2017 IEEE.
PY - 2021/4/1
Y1 - 2021/4/1
N2 - 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.
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.
KW - Behavioral approach
KW - data-driven controllability
KW - system identification
UR - http://www.scopus.com/inward/record.url?scp=85088104553&partnerID=8YFLogxK
U2 - 10.1109/LCSYS.2020.3003770
DO - 10.1109/LCSYS.2020.3003770
M3 - Article
AN - SCOPUS:85088104553
VL - 5
SP - 517
EP - 522
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
SN - 2475-1456
IS - 2
M1 - 9121339
ER -