Evaluation of the Region of Attractions of Higher Dimensional Hyperbolic Systems using the Extended Dynamic Mode Decomposition

TL;DR

This paper introduces a data-driven method using extended dynamic mode decomposition to compute regions of attraction in high-dimensional hyperbolic systems, leveraging Koopman eigenfunctions without requiring explicit models.

Contribution

It presents a novel approach for estimating attraction regions in complex systems through spectral analysis of Koopman operators derived from experimental data.

Findings

Method accurately identifies attraction boundaries in tested systems

Applicable to high-dimensional hyperbolic and polynomial systems

Does not require explicit mathematical models

Abstract

This paper proposes an original methodology to compute the regions of attraction in hyperbolic and polynomial nonlinear dynamical systems using the eigenfunctions of the discrete-time approximation of the Koopman operator given by the extended dynamic mode decomposition algorithm. The proposed method relies on the spectral decomposition of the Koopman operator to build eigenfunctions that capture the boundary of the region of attraction. The algorithm relies solely on data that can be collected in experimental studies and does not require a mathematical model of the system. Two examples of dynamical systems, a population model and a higher dimensional chemical reaction system, allows demonstrating the reliability of the results.