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

arXiv: https://arxiv.org/abs/2309.09817 · HTML: https://mlsanity.com/paper/2309.09817/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2023.

## Built on by (most cited first, 1 of 1)

- [Nonparametric Control Koopman Operators](https://mlsanity.com/paper/2405.07312/) (2024)

## Abstract (arXiv)

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.