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arXiv · 2309.09817

Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators

Zachary Morrison·Moad Abudia·Joel Rosenfeld·Rushikesh Kamalapurar
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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.

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Zachary Morrison, Moad Abudia, Joel Rosenfeld, Rushikesh Kamalapurar. 2023-09-18. Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators. https://doi.org/10.1109/lcsys.2023.3348205

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