Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition
| Autor: | Heiland, J., Unger, B. |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Mathematics
FOS: Electrical engineering electronic engineering information engineering QA1-939 dynamic mode decomposition Mathematics - Numerical Analysis Numerical Analysis (math.NA) Systems and Control (eess.SY) Electrical Engineering and Systems Science - Systems and Control Runge–Kutta method Mathematics system identification |
| Zdroj: | Mathematics, Vol 10, Iss 418, p 418 (2022) mathematics |
| ISSN: | 2227-7390 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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