Data-Driven Safety-Critical Control: Synthesizing Control Barrier Functions With Koopman Operators

Control barrier functions (CBFs) are a powerful tool to guarantee safety of autonomous systems, yet they rely on the computation of control invariant sets, which is notoriously difficult. A backup strategy employs an implicit control invariant set computed by forward integrating the system dynamics....

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Bibliographic Details
Published inIEEE control systems letters Vol. 5; no. 6; pp. 2012 - 2017
Main Authors Folkestad, Carl, Chen, Yuxiao, Ames, Aaron D., Burdick, Joel W.
Format Journal Article
LanguageEnglish
Published IEEE 01.12.2021
Subjects
Collision avoidance
computational methods
Computational modeling
Data models
Dictionaries
Robotics
Safety
Sensitivity
supervisory control
Trajectory
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Summary:Control barrier functions (CBFs) are a powerful tool to guarantee safety of autonomous systems, yet they rely on the computation of control invariant sets, which is notoriously difficult. A backup strategy employs an implicit control invariant set computed by forward integrating the system dynamics. However, this integration is prohibitively expensive for high dimensional systems, and inaccurate in the presence of unmodelled dynamics. We propose to learn discrete-time Koopman operators of the closed-loop dynamics under a backup strategy. This approach replaces forward integration by a simple matrix multiplication, which can mostly be computed offline. We also derive an error bound on the unmodeled dynamics in order to robustify the CBF controller. Our approach extends to multi-agent systems, and we demonstrate the method on collision avoidance for wheeled robots and quadrotors.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2020.3046159