On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
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DOI: 10.1007/s00332-017-9423-0
Abstract: Extended dynamic mode decomposition (EDMD) (Williams et al. in J Nonlinear Sci 25(6):1307–1346, 2015) is an algorithm that approximates the action of the Koopman operator on an N-dimensional subspace of the space of observables by… read more here.
Keywords: dynamic mode; extended dynamic; koopman operator; operator ... See more keywords
Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator.
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DOI: 10.1063/5.0039496
Abstract: Providing efficient and accurate parameterizations for model reduction is a key goal in many areas of science and technology. Here, we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal… read more here.
Keywords: methodology; coupled dynamical; data driven; koopman operator ... See more keywords
Koopman Operator Based Modeling for Quadrotor Control on SE(3)
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DOI: 10.1109/lcsys.2021.3085963
Abstract: In this letter, we propose a Koopman operator based approach to describe the nonlinear dynamics of a quadrotor on $SE(3)$ in terms of an infinite-dimensional linear system which evolves in the space of observables (lifted… read more here.
Keywords: control; koopman operator; operator based; space ... See more keywords
Deep Koopman Operator With Control for Nonlinear Systems
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DOI: 10.1109/lra.2022.3184036
Abstract: Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control methods. However,… read more here.
Keywords: koopman; koopman operator; control; nonlinear systems ... See more keywords
Data-Driven Encoding: A New Numerical Method for Computation of the Koopman Operator
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DOI: 10.1109/lra.2023.3273515
Abstract: This letter presents a data-driven method for constructing a Koopman linear model based on the Direct Encoding (DE) formula. The prevailing methods, Dynamic Mode Decomposition (DMD) and its extensions are based on least squares estimates… read more here.
Keywords: computation; koopman; koopman operator; driven encoding ... See more keywords
Online Koopman Operator Learning to Identify Cross-Coupling Effect of Piezoelectric Tube Scanners in Atomic Force Microscopes
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Industrial Informatics"
DOI: 10.1109/tii.2021.3081418
Abstract: As one of the most significant applications of nanopositioning technology, the tremendous development of atomic force microscopes (AFMs) has been witnessed these years. Essentially, the scanning motions of AFMs are generally driven by piezoelectric tube… read more here.
Keywords: koopman operator; cross; atomic force; cross coupling ... See more keywords
Data-Driven Control of Soft Robots Using Koopman Operator Theory
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DOI: 10.1109/tro.2020.3038693
Abstract: Controlling soft robots with precision is a challenge due to the difficulty of constructing models that are amenable to model-based control design techniques. Koopman operator theory offers a way to construct explicit dynamical models of… read more here.
Keywords: koopman operator; control; soft robots; koopman ... See more keywords
Phase space reconstruction and Koopman operator based linearization of nonlinear model for damage detection of nonlinear structures
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DOI: 10.1177/13694332221082729
Abstract: Vibration responses of structures with inherent nonlinear behaviors can degrade the performance of linear theory based damage detection methods. This paper integrates the phase space reconstruction and Koopman operator to provide a linear representation of… read more here.
Keywords: damage detection; koopman operator; damage;
Koopman Operator Approach to Airdrop Mission Planning Under Uncertainty
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DOI: 10.2514/1.g004277
Abstract: Mission planning for ballistic airdrop requires the selection of optimal control inputs under uncertainty. While significant uncertainty usually exists in airdrop scenarios, current mission plannin... read more here.
Keywords: koopman operator; mission; uncertainty; mission planning ... See more keywords
Approximate Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory
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DOI: 10.2514/1.g005864
Abstract: This work introduces the use of the Koopman Operator Theory to generate analytical solutions for the zonal harmonics problem of a satellite orbiting a non spherical celestial body. Particularly, the solution proposed directly provides the… read more here.
Keywords: harmonics; solution; operator theory; koopman operator ... See more keywords
Koopman Operator Framework for Spectral Analysis and Identification of Infinite-Dimensional Systems
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DOI: 10.3390/math9192495
Abstract: 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… read more here.
Keywords: dimensional systems; infinite dimensional; framework; koopman operator ... See more keywords