Name
Abstract | ||
|---|---|---|
This paper studies the problem of identifying finite-dimensional functional spaces that are close (within a predefined level of accuracy) to being invariant under the application of the Koopman operator. Given a dictionary of functions spanning a finite-dimensional functional space and a set of data snapshots gathered from a potentially nonlinear dynamical system, we define a measure of how close a functional space in the span of the dictionary is to being invariant under the Koopman operator. This measure provides a way of determining the prediction accuracy of the functional space. Given a desired level of accuracy, we propose a numerical algorithm, termed Tunable Symmetric Subspace Decomposition (T-SSD), to find a dictionary of functions with elements in the span of the original dictionary that satisfies it. Starting from the original dictionary, the T-SSD algorithm proceeds by iteratively removing the functions that violate the accuracy bound. We prove that T-SSD converges to a dictionary satisfying the accuracy criteria after a finite number of iterations. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.23919/ACC50511.2021.9483259 | 2021 American Control Conference (ACC) |
Keywords | DocType | ISSN |
data-driven approximation,koopman-invariant subspaces,finite-dimensional functional space,Koopman operator,data snapshots,potentially nonlinear dynamical system,tunable symmetric subspace decomposition | Conference | 0743-1619 |
ISBN | Citations | PageRank |
978-1-7281-9704-3 | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Haseli Masih | 1 | 0 | 1.69 |
| Jorge Cortes | 2 | 1452 | 128.75 |