Characterizing the Predictive Accuracy of Dynamic Mode Decomposition for Data-Driven Control

  title={Characterizing the Predictive Accuracy of Dynamic Mode Decomposition for Data-Driven Control},
  author={Qiugang Lu and Sungho Shin and Victor M. Zavala},

Figures from this paper

Image-Based Model Predictive Control via Dynamic Mode Decomposition
Finite-data error bounds for Koopman-based prediction and control
This paper derives probabilistic bounds for the approximation error and the prediction error depending on the number of training data points and demonstrates the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled.
Guaranteed constraint satisfaction in Koopman-based optimal control
The Koopman framework and an eDMD-based bilinear surrogate modeling approach for control systems are utilized and an error bound on predicted observables is shown to show that satisfaction of tightened constraints in the purely data-based surrogate model implies constraint satisfaction for the original system.


Dynamic Mode Decomposition with Control
This work develops 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 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.
Model reduction using Dynamic Mode Decomposition
Predictive Accuracy of Dynamic Mode Decomposition
This analysis demonstrates the importance of a proper selection of observables, as predicted by the Koopman operator theory, and suggests that DMD is preferable for obtaining a fast prediction with slightly lower accuracy, while POD should be used if the accuracy is paramount.
On dynamic mode decomposition: Theory and applications
A theoretical framework in which dynamic mode decomposition is defined as the eigendecomposition of an approximating linear operator, which generalizes DMD to a larger class of datasets, including nonsequential time series, and shows that under certain conditions, DMD is equivalent to LIM.
Online dynamic mode decomposition for time-varying systems
This work provides an efficient method for computing DMD in real time, updating the approximation of a system's dynamics as new data becomes available, and is effective at capturing the dynamics of surface pressure measurements in the flow over an unsteady separation bubble.
Evaluating the accuracy of the dynamic mode decomposition
This work proposes a new criterion to estimate the accuracy of DMD on a mode-by-mode basis, by estimating how closely each individual DMD eigen function approximates the corresponding Koopman eigenfunction, and successfully identifies modes of high accuracy when applying DMD to data from experiments in fluids.
An error analysis of the dynamic mode decomposition
Dynamic mode decomposition (DMD) is a new diagnostic technique in fluid mechanics which is growing in popularity. A powerful analysis tool, it has great potential for measuring the spatial and
POD a-posteriori error estimates for linear-quadratic optimal control problems
An a-posteriori analysis for the method of proper orthogonal decomposition (POD) applied to optimal control problems governed by parabolic and elliptic PDEs is deduced.
Dynamic mode decomposition of numerical and experimental data
  • P. Schmid
  • Physics, Engineering
    Journal of Fluid Mechanics
  • 2010
The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information