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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Vehicular Applications of Koopman Operator Theory—A Survey [PDF]
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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A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition [PDF]
Journal of nonlinear science, 2014 The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of nonlinear ...
Kevrekidis, Ioannis G. +2 more
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Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control. [PDF]
PLoS ONE, 2016 In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions.
Steven L Brunton +3 more
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A Koopman operator-based prediction algorithm and its application to COVID-19 pandemic and influenza cases. [PDF]
Sci RepFuture state prediction for nonlinear dynamical systems is a challenging task. Classical prediction theory is based on a, typically long, sequence of prior observations and is rooted in assumptions on statistical stationarity of the underlying stochastic
Mezić I +8 more
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Koopman Operator–Based Knowledge-Guided Reinforcement Learning for Safe Human–Robot Interaction [PDF]
Frontiers in Robotics and AI, 2022 We developed a novel framework for deep reinforcement learning (DRL) algorithms in task constrained path generation problems of robotic manipulators leveraging human demonstrated trajectories.
Anirban Sinha, Yue Wang
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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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Koopman operator-based model reduction for switched-system control of PDEs [PDF]
, 2019 We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables.
Sebastian Peitz, Stefan Klus
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Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation laws [PDF]
Physical Review ResearchAccurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently.
Jingdong Zhang, Qunxi Zhu, Wei Lin
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Temporally-consistent koopman autoencoders for forecasting dynamical systems [PDF]
Scientific ReportsAbsence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems.
Indranil Nayak +4 more
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