On Numerical Approximations of the Koopman Operator by Igor Mezić

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Autoencoding for the "Good Dictionary" of eigenpairs of the Koopman operator by Neranjaka Jayarathne, Erik M. Bollt

“…Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through the Koopman operator(KO) analysis. However, computing Koopman eigenpairs for high-dimensional observable data can be inefficient. …”
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The Koopman Operator in Systems and Control : Concepts, Methodologies, and Applications / by Mauroy, Alexandre, editor 632452, Mezic, Igor, editor 456303, Susuki, Yoshihiko, editor 632453

Data-driven Static Equivalence with Physics-informed Koopman Operators by Wei Lin, Changhong Zhao, Maosheng Gao, C. Y. Chung

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Data-Driven Predictive Control of Interconnected Systems Using the Koopman Operator by Duvan Tellez-Castro, Camilo Garcia-Tenorio, Eduardo Mojica-Nava, Jorge Sofrony, Alain Vande Wouwer

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A quantitative analysis of Koopman operator methods for system identification and predictions by Zhang, Christophe, Zuazua, Enrique

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Vehicular Applications of Koopman Operator Theory—A Survey by Waqas A. Manzoor, Samir Rawashdeh, Alireza Mohammadi

“…Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. …”
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Koopman Operator and Path Integral of Quantum Free-Electron Laser Model by Alexander Iomin

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Koopman Operator Framework for Spectral Analysis and Identification of Infinite-Dimensional Systems by Alexandre Mauroy

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Applications of the Koopman Operator: Novel Methods and Formulations for Lifted Linear Models by Ng, Jerry

“…We then discuss the methods for constructing the Koopman Operator. Specifically, we alleviate the pitfalls of current data-driven methods for construction of the Koopman Operator through the use of a data-driven formulation of Direct Encoding, which is based on integration. …”
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Network Structure Identification Based on Measured Output Data Using Koopman Operators by Zhuanglin Mei, Toshiki Oguchi

“…In the second step, we define the dynamical inputs as new variables and identify the dynamics of the network system with measured output data using Koopman operators. Finally, we extract the network structure from the identified dynamics as the information transmitted via the network. …”
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Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation laws by Jingdong Zhang, Qunxi Zhu, Wei Lin

“…Here, for the Hamiltonian mechanics, we propose the Hamiltonian neural Koopman operator (HNKO), integrating the knowledge of mathematical physics in learning the Koopman operator, and making it automatically sustain and even discover the conservation laws. …”
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Stability Analysis of Parameter Varying Genetic Toggle Switches Using Koopman Operators by Jamiree Harrison, Enoch Yeung

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Approximate Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory by Arnas, David, Linares, Richard

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Dynamics Near the Three-Body Libration Points via Koopman Operator Theory by Servadio, Simone, Arnas, David, Linares, Richard

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Koopman Operator Theory Applied to Lambert’s Problem with a Spectral Behavior Analysis by Pasiecznik, Julia

“…Furthermore, the Koopman Operator enables the computation of these solutions with low computational complexity. …”
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Koopman operator based model predictive control for trajectory tracking of an omnidirectional mobile manipulator by Xuehong Zhu, Chengjun Ding, Lizhen Jia, Yubo Feng

“…This paper designs a Koopman operator based model predictive control (MPC) scheme for trajectory tracking control of an OMM. …”
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Data-driven Estimation for a Region of Attraction for Transient Stability Using the Koopman Operator by Le Zheng, Xin Liu, Yanhui Xu, Wei Hu, Chongru Liu

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Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory by Yuzuru Kato, Jinjie Zhu, Wataru Kurebayashi, Hiroya Nakao

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Data-driven moving horizon state estimation of nonlinear processes using Koopman operator by Yin, Xunyuan, Qin, Yan, Liu, Jinfeng, Huang, Biao

“…In this paper, a data-driven constrained state estimation method is proposed for nonlinear processes. Within the Koopman operator framework, we propose a data-driven model identification procedure for state estimation based on the algorithm of extended dynamic mode decomposition, which seeks an optimal approximation of the Koopman operator for a nonlinear process in a higher-dimensional space that correlates with the original process state-space via a prescribed nonlinear coordinate transformation. …”
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