ON DYNAMIC MODE DECOMPOSITION: THEORY AND …

Manuscript submitted to the Journal of Computational DynamicsON DYNAMIC MODE DECOMPOSITION: THEORY AND APPLICATIONSJ onathan H. Tu, Clarence W. Rowley, Dirk M. Luchtenburg,Dept. of Mechanical and Aerospace EngineeringPrinceton UniversityPrinceton, NJ 08544, USAS teven L. Brunton, and J. Nathan KutzDept. of Applied MathematicsUniversity of WashingtonSeattle, WA 98195, introduced in the fluid mechanics community, dynamicmode decomposition (DMD) has emerged as a powerful tool for analyzing thedynamics of nonlinear systems. However, existing DMD THEORY deals primarilywith sequential time series for which the measurement dimension is much largerthan the number of measurements taken. We present a theoretical frameworkin which we define DMD as the eigendecomposition of an approximating lin-ear operator. This generalizes DMD to a larger class of datasets, includingnonsequential time series.

known methods, speci cally the eigensystem realization algorithm (ERA) and linear inverse modeling (LIM). The ERA is a control-theoretic method for system iden-ti cation of linear systems [27,28,29]. We show that when computed from the same data, DMD eigenvalues reduce to poles of an ERA model. This connection

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  System, Linear, Dome, Methods, Dynamics, Theory, Theory and, Decomposition, Linear systems, Dynamic mode decomposition

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