Summary
International Symposium on Nonlinear Theory and its Applications
2017
Session Number:A1L-A
Session:
Number:A1L-A-1
On the Computation of Isostables, Isochrons and Other Spectral Objects of the Koopman Operator Using the Dynamic Mode Decomposition
Igor Mezic, Hassan Arbabi,
pp.1-4
Publication Date:2017/12/4
Online ISSN:2188-5079
Summary:
Two types of state-space objects - isostables and isochrons - obtained as level sets of Koopman operator eigenfunctions, have recently been shown to be of utility in nonlinear control theory. Algorithms to compute these are in the class of the so-called Dynamic Mode Decomposition (DMD) algorithms or Generalized Laplace Analysis (GLA) algorithms. It is interesting to explore the relationship between these two, which is what we pursue in this paper. We do this in the context more general than isochrons and isostables, deriving results on the relationship of the full Koopman Mode Decomposition with objects computed in DMD, using the fact that GLA is known to be an exact algorithm in the infinite time limit. We also show that finite-dimensional DMD approximations of Koopman eigenfunctions are in the Koopman operator pseudospectrum.