Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Two roads to Koopman operator theory for
control: infinite input sequences and operator families
M. Haseli, I. Mezić, J. Cortés
IEEE Transactions on Automatic Control, submitted
Abstract
The Koopman operator, originally defined for dynamical systems
without input, has inspired many applications in control. Yet, the
theoretical foundations underpinning this progress in control remain
underdeveloped. This paper investigates the theoretical structure
and connections between two extensions of Koopman theory to control:
(i) Koopman operator via infinite input sequences and (ii) the
Koopman control family. Although these frameworks encode system
information in fundamentally different ways, we show that under
certain conditions on the function spaces they operate on, they are
equivalent. The equivalence is both in terms of the actions of the
Koopman-based formulations in each framework
as well as the function values on the system trajectories. Our
analysis provides constructive tools to translate between the
frameworks, offering a unified perspective for Koopman methods in
control.
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Mechanical and Aerospace Engineering,
University of California, San Diego
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Ph: 1-858-822-7930
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cortes at ucsd.edu
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