Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition

Jan Heiland and Benjamin Unger
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Jan Heiland: Max Planck Institute for Dynamics of Complex Technical Systems, 39106 Magdeburg, Germany
Benjamin Unger: Stuttgart Center for Simulation Science, University of Stuttgart, 70563 Stuttgart, Germany

Mathematics, 2022, vol. 10, issue 3, 1-13

Abstract: 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.

Keywords: dynamic mode decomposition; system identification; Runge–Kutta method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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