date: 2022-01-28T09:50:20Z
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pdf:docinfo:title: Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition
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Keywords: dynamic mode decomposition; system identification; Runge?Kutta method
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subject: Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge?Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge?Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings.
dc:creator: Jan Heiland and Benjamin Unger
dcterms:created: 2022-01-28T09:44:25Z
Last-Modified: 2022-01-28T09:50:20Z
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title: Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition
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pdf:docinfo:keywords: dynamic mode decomposition; system identification; Runge?Kutta method
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dc:title: Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition
modified: 2022-01-28T09:50:20Z
cp:subject: Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge?Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge?Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings.
pdf:docinfo:subject: Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge?Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge?Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings.
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pdf:docinfo:creator: Jan Heiland and Benjamin Unger
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creator: Jan Heiland and Benjamin Unger
meta:author: Jan Heiland and Benjamin Unger
dc:subject: dynamic mode decomposition; system identification; Runge?Kutta method
meta:creation-date: 2022-01-28T09:44:25Z
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meta:keyword: dynamic mode decomposition; system identification; Runge?Kutta method
Author: Jan Heiland and Benjamin Unger
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