SIAM Journal on Applied Dynamical Systems· 2016Q1
Dynamic Mode Decomposition with Control
- 1,084citations
- Q1SCImago
- 2016year
Short summary
A new data-driven method, Dynamic Mode Decomposition with Control (DMDc), extends standard DMD to accurately model input-output relationships in complex, high-dimensional systems by distinguishing underlying dynamics from actuation effects.
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Key points
- DMDc is a new method extending Dynamic Mode Decomposition (DMD) to incorporate control effects.
- It extracts accurate input-output models from high-dimensional systems using only time-series data.
- DMDc disambiguates underlying dynamics from actuation effects, unlike standard DMD.
- The method is demonstrated on complex systems, including a model for infectious disease analysis with mass vaccination.
AI-generated from the title and abstract; the full text is not read.
Abstract
We develop a new method which extends dynamic mode decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear analysis to nonlinear operator theory, and provides an equation-free architecture which is compatible with compressive sensing. In actuated systems, DMD is incapable of producing an input-output model; moreover, the dynamics and the modes will be corrupted by external forcing. Our new method, dynamic mode decomposition with control (DMDc), capitalizes on all of the advantages of DMD and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models. The method is data-driven in that it does not require knowledge of the underlying governing equations---only snapshots in time of observables and actuation data from historical, experimental, or black-box simulations. We demonstrate the method on high-dimensional dynamical systems, including a model with relevance to the analysis of infectious disease data with mass vaccination (actuation).
The authors' abstract, as published at the source. SIAM Journal on Applied Dynamical Systems, 2016 · DOI ↗
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Field: Statistical and Nonlinear Physics
Statistical and Nonlinear PhysicsPhysics and Astronomy