Results 51 to 60 of about 1,745 (187)

Decompositions of Dynamical Systems Induced by the Koopman Operator [PDF]

Analysis Mathematica, 2021
For a topological dynamical system we characterize the decomposition of the state space induced by the fixed space of the corresponding Koopman operator. For this purpose, we introduce a hierarchy of generalized orbits and obtain the finest decomposition of the state space into absolutely Lyapunov stable sets. Analogously to the measure-preserving case,
openaire   +3 more sources

Neural Koopman forecasting for critical transitions in infrastructure networks

Intelligent Systems with Applications
We develop a data-driven framework for long-term forecasting of stochastic dynamics on evolving networked infrastructure systems using neural approximations of Koopman operators.
Ramen Ghosh
doaj   +1 more source

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 ...
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Short-Term Voltage Stability Prediction for Power Systems Based on a Dominant Koopman Operator-Enhanced MLE

IEEE Access
Short-term voltage stability (STVS) prediction is a critical technology for modern power systems with high penetration of renewable energy resources. To address the limitations of the traditional maximum Lyapunov exponent (MLE) in handling short-time ...
Han Gao, Deyou Yang, Yanling Lv, Lixin Wang   +3 more
doaj   +1 more source

Koopman Operator Approximation under Negative Imaginary Constraints [PDF]

, 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 letter, we propose a data-driven
Meskin, Nader, Ilyasse Aksikas, Nader Meskin, Mohamed A. Mabrok, Aksikas, Ilyasse, Mabrok, Mohamed A.   +5 more
core   +1 more source

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Physical Review Research, 2020
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman–von Neumann formulation of classical mechanics.
Ilon Joseph
doaj   +1 more source

Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition

Automation, 2023
This paper provides the theoretical foundation for the approximation of the regions of attraction in hyperbolic and polynomial systems based on the eigenfunctions deduced from the data-driven approximation of the Koopman operator.
Camilo Garcia-Tenorio, Duvan Tellez-Castro, Eduardo Mojica-Nava, Alain Vande Wouwer   +3 more
doaj   +1 more source

Koopman-Based Control System for Quadrotors in Noisy Environments

IEEE Access
It is well known that identification of the complete system dynamics is challenging, especially in noisy environments. The Koopman operator theory provides a linear representation of a nonlinear system using only the input/output data acquired from the ...
Yuna Oh, Myoung Hoon Lee, Jun Moon
doaj   +1 more source

Stabilizing RED Using the Koopman Operator

IEEE Signal Processing Letters
The widely used RED (Regularization-by-Denoising) framework uses pretrained denoisers as implicit regularizers for model-based reconstruction. Although RED generally yields high-fidelity reconstructions, the use of black-box denoisers can sometimes lead to instability.
Shraddha Chavan, Kunal N. Chaudhury
openaire   +2 more sources

Deep learning for Koopman operator approximations for control

, 2021
The focus of this thesis is on combining the potential of Koopman operator theory with that of deep learning. This research topic has gained more and more interest in the scientific community in the last few years and is appealing for its great potential
Hader, Magdalena
core   +1 more source