Scalable Extended Dynamic Mode Decomposition Using Random Kernel Approximation [PDF]
SIAM Journal on Scientific Computing, 2019 The Koopman operator is a linear, infinite-dimensional operator that governs the dynamics of system observables; Extended Dynamic Mode Decomposition (EDMD) is a data-driven method for approximating the Koopman operator using functions (features) of the system state snapshots.
Anthony M. DeGennaro, Nathan M. Urban
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On Analytical Construction of Observable Functions in Extended Dynamic Mode Decomposition for Nonlinear Estimation and Prediction [PDF]
IEEE Control Systems Letters, 2021 We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of observable functions is fundamental for the application of EDMD to nonlinear problems arising in systems and control ...
Marcos Netto +3 more
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Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017 Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD)51 and its generalization, the extended-DMD (EDMD), are becoming increasingly popular in practical applications.
Qianxiao Li +3 more
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Data-Driven MPC With Stability Guarantees Using Extended Dynamic Mode Decomposition
IEEE Transactions on Automatic Control18 pages, 3 ...
Lea Bold +3 more
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Orthogonal Polynomial Approximation and Extended Dynamic Mode Decomposition in Chaos
SIAM Journal on Numerical AnalysisExtended Dynamic Mode Decomposition (EDMD) is a data-driven tool for forecasting and model reduction of dynamics, which has been extensively taken up in the physical sciences. While the method is conceptually simple, in deterministic chaos it is unclear what its properties are or even what it converges to.
Caroline L Wormell
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Analysis of the ROA of an anaerobic digestion process via data-driven Koopman operator
Nonlinear Engineering, 2021 Nonlinear biochemical systems such as the anaerobic digestion process experience the problem of the multi-stability phenomena, and thus, the dynamic spectrum of the system has several undesired equilibrium states.
Garcia-Tenorio Camilo +3 more
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Data-Driven Predictive Control of Interconnected Systems Using the Koopman Operator
Actuators, 2022 Interconnected systems are widespread in modern technological systems. Designing a reliable control strategy requires modeling and analysis of the system, which can be a complicated, or even impossible, task in some cases.
Duvan Tellez-Castro +4 more
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Extended dynamic mode decomposition for two paradigms of non-linear dynamical systems
Journal of the Franklin Institute, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
John Leventides +2 more
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IEEE Access, 2022 This paper presents an active disturbance rejection control (ADRC) method for modular robot manipulators (MRMs) based on extended state observer (ESO), which solves the problem of trajectory tracking when modular robot manipulators facing the emotional ...
Xiao Pang +3 more
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A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition [PDF]
Journal of Nonlinear Science, 2015 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 dynamical systems.
Matthew O. Williams +2 more
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