Results 21 to 30 of about 13,618 (231)
Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?
Mathematics, 2021 This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field
Erik M. Bollt, Shane D. Ross
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Representer Theorem for Learning Koopman Operators
IEEE Transactions on Automatic Control, 2023 In this work, the problem of learning Koopman operator of a discrete-time autonomous system is considered. The learning problem is formulated as a constrained regularized empirical loss minimization in the infinite-dimensional space of linear operators.
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Measurement + Control, 2022 The dynamic modeling and control of omni-directional mobile manipulators (OMM) are challenging since they are highly nonlinear, strongly coupled, and multi-input multi-output uncertainty systems.
Xuehong Zhu +5 more
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Sparsity structures for Koopman operators
, 2021 We present a decomposition of the Koopman operator based on the sparse structure of the underlying dynamical system, allowing one to consider the system as a family of subsystems interconnected by a graph. Using the intrinsic properties of the Koopman operator, we show that eigenfunctions for the subsystems induce eigenfunctions for the whole system ...
Schlosser, Corbinian, Korda, Milan
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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.
Črnjarić-Žic, Nelida +2 more
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Koopman Operator Approximation under Negative Imaginary Constraints
IEEE Control Systems Letters, 2023 Nonlinear Negative Imaginary (NI) systems arise in various engineering applications, such as controlling flexible structures and air vehicles. However, unlike linear NI systems, their theory is not well-developed. In this paper, we propose a data-driven method for learning a lifted linear NI dynamics that approximates a nonlinear dynamical system using
Mohamed A. Mabrok +2 more
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Koopman Operator and its Approximations for Systems with Symmetries [PDF]
, 2019 Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations.
Crutchfield, James P. +4 more
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Identification of the Madden–Julian Oscillation With Data‐Driven Koopman Spectral Analysis
Geophysical Research Letters, 2023 The Madden‐Julian Oscillation (MJO), the dominant mode of tropical intraseasonal variability, is commonly identified using the realtime multivariate MJO (RMM) index based on joint empirical orthogonal function (EOF) analysis of near‐equatorial upper and ...
Benjamin R. Lintner +3 more
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Stable data‐driven Koopman predictive control: Concentrated solar collector field case study
IET Control Theory & Applications, 2023 Non‐linearity is an inherent feature of practical systems. Although there have been significant advances in the control of nonlinear systems, the proposed methods often require considerable computational resources or rely on local linearization around ...
Tahereh Gholaminejad, Ali Khaki‐Sedigh
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Complexity, 2018 We consider the application of Koopman theory to nonlinear partial differential equations and data-driven spatio-temporal systems. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate ...
J. Nathan Kutz +2 more
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