An Alternative Framework for Dynamic Mode Decomposition with Control
Dynamic mode decomposition with control (DMDc) is a widely used technique for analyzing dynamic systems influenced by external control inputs. It is a recent development and an extension of dynamic mode decomposition (DMD) tailored for input–output systems. In this work, we investigate and analyze a...
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MDPI AG
2025-05-01
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| author | Gyurhan Nedzhibov |
| author_facet | Gyurhan Nedzhibov |
| author_sort | Gyurhan Nedzhibov |
| collection | DOAJ |
| description | Dynamic mode decomposition with control (DMDc) is a widely used technique for analyzing dynamic systems influenced by external control inputs. It is a recent development and an extension of dynamic mode decomposition (DMD) tailored for input–output systems. In this work, we investigate and analyze an alternative approach for computing DMDc. Compared to the traditional formulation, the proposed method restructures the computation by decoupling the influence of the state and control components, allowing for a more modular and interpretable implementation. The algorithm avoids compound operator approximations typical of standard approaches, which makes it potentially more efficient in real-time applications or systems with streaming data. The new scheme aims to improve computational efficiency while maintaining the reliability and accuracy of the decomposition. We provide a theoretical proof that the dynamic modes produced by the proposed method are exact eigenvectors of the corresponding Koopman operator. Compared to the standard DMDc approach, the new algorithm is shown to be more efficient, requiring fewer calculations and less memory. Numerical examples are presented to demonstrate the theoretical results and illustrate potential applications of the modified approach. The results highlight the promise of this alternative formulation for advancing data-driven modeling and control in various engineering and scientific domains. |
| format | Article |
| id | doaj-art-c5c7acf05aee4f019a79c317f7673572 |
| institution | Kabale University |
| issn | 2673-9909 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| series | AppliedMath |
| spelling | doaj-art-c5c7acf05aee4f019a79c317f76735722025-08-20T03:32:27ZengMDPI AGAppliedMath2673-99092025-05-01526010.3390/appliedmath5020060An Alternative Framework for Dynamic Mode Decomposition with ControlGyurhan Nedzhibov0Faculty of Mathematics and Computer Science, Konstantin Preslavsky University of Shumen, 9700 Shumen, BulgariaDynamic mode decomposition with control (DMDc) is a widely used technique for analyzing dynamic systems influenced by external control inputs. It is a recent development and an extension of dynamic mode decomposition (DMD) tailored for input–output systems. In this work, we investigate and analyze an alternative approach for computing DMDc. Compared to the traditional formulation, the proposed method restructures the computation by decoupling the influence of the state and control components, allowing for a more modular and interpretable implementation. The algorithm avoids compound operator approximations typical of standard approaches, which makes it potentially more efficient in real-time applications or systems with streaming data. The new scheme aims to improve computational efficiency while maintaining the reliability and accuracy of the decomposition. We provide a theoretical proof that the dynamic modes produced by the proposed method are exact eigenvectors of the corresponding Koopman operator. Compared to the standard DMDc approach, the new algorithm is shown to be more efficient, requiring fewer calculations and less memory. Numerical examples are presented to demonstrate the theoretical results and illustrate potential applications of the modified approach. The results highlight the promise of this alternative formulation for advancing data-driven modeling and control in various engineering and scientific domains.https://www.mdpi.com/2673-9909/5/2/60dynamicmode decomposition with controlKoopman operatorDMDc methoddynamical systemsequation-free |
| spellingShingle | Gyurhan Nedzhibov An Alternative Framework for Dynamic Mode Decomposition with Control AppliedMath dynamicmode decomposition with control Koopman operator DMDc method dynamical systems equation-free |
| title | An Alternative Framework for Dynamic Mode Decomposition with Control |
| title_full | An Alternative Framework for Dynamic Mode Decomposition with Control |
| title_fullStr | An Alternative Framework for Dynamic Mode Decomposition with Control |
| title_full_unstemmed | An Alternative Framework for Dynamic Mode Decomposition with Control |
| title_short | An Alternative Framework for Dynamic Mode Decomposition with Control |
| title_sort | alternative framework for dynamic mode decomposition with control |
| topic | dynamicmode decomposition with control Koopman operator DMDc method dynamical systems equation-free |
| url | https://www.mdpi.com/2673-9909/5/2/60 |
| work_keys_str_mv | AT gyurhannedzhibov analternativeframeworkfordynamicmodedecompositionwithcontrol AT gyurhannedzhibov alternativeframeworkfordynamicmodedecompositionwithcontrol |