Jorge Cortés


Data-driven approximation of Koopman-invariant subspaces with tunable accuracy
M. Haseli, J. Cortés
American Control Conference, New Orleans, Louisiana, 2021, to appear


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.


Mechanical and Aerospace Engineering, University of California, San Diego
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