TY - GEN

T1 - Behavioral uncertainty quantification for data-driven control

AU - Padoan, Alberto

AU - Coulson, Jeremy

AU - Van Waarde, Henk J.

AU - Lygeros, John

AU - Dorfler, Florian

N1 - Funding Information:
A. Padoan, J. Coulson, J. Lygeros, F. Dörfler are with the Department of Information Technology and Electrical Engineering at ETH Zürich, Zürich, Switzerland {apadoan, jcoulson, lygeros, dorfler}@control.ee.ethz.ch. H. J. van Waarde is with the Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, The Netherlands. h.j.van.waarde@rug.nl. Research supported by the Swiss National Science Foundation under the NCCR Automation.
Publisher Copyright:
© 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - This paper explores the problem of uncertainty quantification in the behavioral setting for data-driven control. Building on classical ideas from robust control, the problem is regarded as that of selecting a metric which is best suited to a data-based description of uncertainties. Leveraging on Willems' fundamental lemma, restricted behaviors are viewed as subspaces of fixed dimension, which may be represented by data matrices. Consequently, metrics between restricted behaviors are defined as distances between points on the Grassmannian, i.e., the set of all subspaces of equal dimension in a given vector space. A new metric is defined on the set of restricted behaviors as a direct finite-time counterpart of the classical gap metric. The metric is shown to capture parametric uncertainty for the class of autoregressive (AR) models. Numerical simulations illustrate the value of the new metric with a data-driven mode recognition and control case study.

AB - This paper explores the problem of uncertainty quantification in the behavioral setting for data-driven control. Building on classical ideas from robust control, the problem is regarded as that of selecting a metric which is best suited to a data-based description of uncertainties. Leveraging on Willems' fundamental lemma, restricted behaviors are viewed as subspaces of fixed dimension, which may be represented by data matrices. Consequently, metrics between restricted behaviors are defined as distances between points on the Grassmannian, i.e., the set of all subspaces of equal dimension in a given vector space. A new metric is defined on the set of restricted behaviors as a direct finite-time counterpart of the classical gap metric. The metric is shown to capture parametric uncertainty for the class of autoregressive (AR) models. Numerical simulations illustrate the value of the new metric with a data-driven mode recognition and control case study.

UR - http://www.scopus.com/inward/record.url?scp=85147006792&partnerID=8YFLogxK

U2 - 10.1109/CDC51059.2022.9993002

DO - 10.1109/CDC51059.2022.9993002

M3 - Conference contribution

AN - SCOPUS:85147006792

SN - 978-1-6654-6762-9

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4726

EP - 4731

BT - 2022 IEEE 61st Conference on Decision and Control, CDC 2022

PB - IEEE

T2 - 61st IEEE Conference on Decision and Control, CDC 2022

Y2 - 6 December 2022 through 9 December 2022

ER -