Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators
Abstract
Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analysis. In this paper, we provide a novel representation for discrete-time control-affine nonlinear dynamical systems as linear operators acting on a Hilbert space. We also demonstrate that this representation can be used to predict the behavior of the closed-loop system given a known feedback law using recorded snapshots of the system state resulting from arbitrary, potentially open-loop control inputs. We thereby extend the predictive capabilities of dynamic mode decomposition to discrete-time nonlinear systems that are affine in control. We validate the method using two numerical experiments by predicting the response of a controlled Duffing oscillator to a known feedback law, as well as demonstrating the advantage of the developed method relative to existing techniques in the literature.
Cite
@article{arxiv.2309.09817,
title = {Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators},
author = {Zachary Morrison and Moad Abudia and Joel Rosenfeld and Rushikesh Kamalapurar},
journal= {arXiv preprint arXiv:2309.09817},
year = {2024}
}