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This paper introduces the Koopman Control Family (KCF), a mathematical framework for modeling general (not necessarily control-affine) discrete-time nonlinear control systems with the aim of providing a solid theoretical foundation for the use of Koopman-based methods in systems with inputs.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
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Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
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Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
S. L. Brunton, B. W. Brunton, J. L. Proctor, and J. N. Kutz · 2016
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Global stability analysis using the eigenfunctions of the Koopman operator
A. Mauroy and I. Mezić · 2016
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Dynamic mode decomposition with control
J. L. Proctor, S. L. Brunton, and J. N. Kutz · 2016
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Pulse-based control using Koopman operator under parametric uncertainty
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Learning Koopman invariant subspaces for dynamic mode decomposition
N. Takeishi, Y. Kawahara, and T. Yairi · 2017
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Feedback stabilization using Koopman operator
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Koopman operator family spectrum for nonautonomous systems
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Optimal control formulation of pulse-based control using Koopman operator
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On the equivalence of contraction and Koopman approaches for nonlinear stability and control
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Switched nonlinear systems in the Koopman operator framework: Toward a Lie-algebraic condition for uniform stability
C. M. Zagabe and A. Mauroy · 2021
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Safe control design for unknown nonlinear systems with Koopman-based fixed-time identification
M. Black and D. Panagou · 2022
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Koopman-based neural Lyapunov functions for general attractors
S. A. Deka, A. M. Valle, and C. J. Tomlin · 2022
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Bilinearization, reachability, and optimal control of control-affine nonlinear systems: A Koopman spectral approach
D. Goswami and D. A. Paley · 2022
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Data-driven control of soft robots using Koopman operator theory
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Data-driven safety-critical control: Synthesizing control barrier functions with Koopman operators
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Optimal construction of Koopman eigenfunctions for prediction and control
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Data-driven model predictive control using interpolated Koopman generators
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Learning Koopman eigenfunctions and invariant subspaces from data: Symmetric Subspace Decomposition
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Koopman form of nonlinear systems with inputs
L. C. Iacob, R. Tóth, and M. Schoukens · 2022
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Data-driven feedback stabilisation of nonlinear systems: Koopman-based model predictive control
A. Narasingam, S. H. Son, and J. S. Kwon · 2022
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Reachability analysis using spectrum of Koopman operator
B. Umathe, D. Tellez-Castro, and U. Vaidya · 2022
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Koopman-inspired implicit backward reachable sets for unknown nonlinear systems
H. Balim, A. Aspeel, Z. Liu, and N. Ozay · 2023
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Learning switched Koopman models for control of entity-based systems
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Finite-data error bounds for Koopman-based prediction and control
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W. Sharpless, N. Shinde, M. Kim, Y. T. Chow, and S. Herbert · 2023
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