Results 31 to 40 of about 1,082,543 (312)
Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces [PDF]
Neural Information Processing Systems, 2022 We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator.
V. Kostić +5 more
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Koopman Operator Framework for Spectral Analysis and Identification of Infinite-Dimensional Systems
Mathematics, 2021 We consider the Koopman operator theory in the context of nonlinear infinite-dimensional systems, where the operator is defined over a space of bounded continuous functionals. The properties of the Koopman semigroup are described and a finite-dimensional
Alexandre Mauroy
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Feedback Stabilization Using Koopman Operator [PDF]
2018 IEEE Conference on Decision and Control (CDC), 2018 Accepted for IEEE Conference on Decision and Control(CDC ...
Huang, Bowen, Ma, Xu, Vaidya, Umesh
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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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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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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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