Dynamic mode decomposition with control
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Publication:2790855
DOI10.1137/15M1013857zbMATH Open1334.65199arXiv1409.6358OpenAlexW1723433682MaRDI QIDQ2790855
Author name not available (Why is that?)
Publication date: 8 March 2016
Published in: (Search for Journal in Brave)
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 of state 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).
Full work available at URL: https://arxiv.org/abs/1409.6358
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