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On a stochastic fundamental lemma and its use for data-driven optimal control
Publikationstyp
Journal Article
Publikationsdatum
2023-10-01
Sprache
English
Author
Enthalten in
Volume
68
Issue
10
Start Page
5922
End Page
5937
Citation
IEEE Transactions on Automatic Control 68 (10): 5922-5937 (2023-10-01)
Publisher DOI
Scopus ID
Publisher
IEEE
Data-driven control based on the fundamental lemma by Willems et al. is frequently considered for deterministic linear time invariant (LTI) systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect the dynamics. In this article, we leverage polynomial chaos expansions to extend the deterministic fundamental lemma toward stochastic systems. This extension allows to predict future statistical distributions of the inputs and outputs for stochastic LTI systems in data-driven fashion, i.e., based on the knowledge of previously recorded input-output-disturbance data and of the disturbance distribution we perform data-driven uncertainty propagation. Finally, we analyze data-driven stochastic optimal control problems and we propose a conceptual framework for data-driven stochastic predictive control. Numerical examples illustrate the efficacy of the proposed concepts.
Schlagworte
Data-driven control
fundamental lemma
learning systems
model predictive control
optimal control
polynomial chaos
stochastic systems
uncertainty quantification
DDC Class
530: Physics