### Jorge Cortés

#### Professor

Data-driven approximation of Koopman-invariant subspaces with tunable accuracy

M. Haseli, J. Cortés

Proceedings of the American Control Conference, New Orleans, Louisiana, 2021, pp. 469-474

***2021 ACC Best Student Paper Award***

### 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. A simulation example
demonstrates the efficacy of our method.

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Mechanical and Aerospace Engineering,
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