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 -