Results 11 to 20 of about 472,452 (242)
Vehicular Applications of Koopman Operator Theory—A Survey
IEEE Access, 2023 Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering purposes.
Waqas A. Manzoor +2 more
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Closed-loop Koopman operator approximation [PDF]
Machine Learning: Science and TechnologyThis paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in terms of an ...
Steven Dahdah, James Richard Forbes
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Koopman operator for Burgers's equation [PDF]
Physical Review Fluids, 2021 The Koopman decomposition of the Burgers' flow is explicitly derived, the frequencies and the coefficients of this decomposition are identified as eigenvalues and eigenfunctionals of the Koopman operator, and the convergence of the Koopman decomposition is proven for $tg0$ for small Cauchy data, and up to $t=0$ for regular Cauchy data.
Mikhael Balabane +2 more
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Robust Approximation of the Stochastic Koopman Operator
SIAM Journal on Applied Dynamical Systems, 2022 20 pages, six ...
Igor Mezic, Mathias Wanner
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Dynamical systems and complex networks: a Koopman operator perspective [PDF]
Journal of Physics: ComplexityThe Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept—representing highly nonlinear dynamical systems by infinite-dimensional linear operators—has been known for a long time, the ...
Stefan Klus, Nataša Djurdjevac Conrad
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On Numerical Approximations of the Koopman Operator
Mathematics, 2022 We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode Decomposition-type methods in the context of Finite Section theory of infinite dimensional operators, and provide an example of a ...
Igor Mezic
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Koopman Operator Spectrum for Random Dynamical Systems [PDF]
Journal of Nonlinear Science, 2019 In this paper we consider the Koopman operator associated with the discrete and the continuous time random dynamical system (RDS). We provide results that characterize the spectrum and the eigenfunctions of the stochastic Koopman operator associated with different types of linear RDS.
Nélida Črnjarić +2 more
exaly +6 more sources
Propagation of Uncertainty with the Koopman Operator [PDF]
2024 27th International Conference on Information Fusion (FUSION)27th Conference of Information Fusion ID ...
Servadio, Simone +4 more
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Deep Koopman Operator With Control for Nonlinear Systems [PDF]
IEEE Robotics and Automation Letters, 2022 Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control methods. However, designing an appropriate Koopman embedding function remains a challenging task.
Haojie Shi, Max Q.-H. Meng
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Koopman operator and its approximations for systems with symmetries [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019 Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, often described by complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and to simplify their analysis.
Anastasiya Salova +4 more
openaire +8 more sources