Deep Koopman Learning of Nonlinear Time-Varying Systems

TL;DR

This paper introduces a deep learning-based Koopman operator approach to approximate nonlinear time-varying systems with linear models, enabling efficient analysis and control with small approximation errors.

Contribution

It develops a data-driven method combining Koopman operators and neural networks to model nonlinear time-varying systems as linear time-varying systems.

Findings

Achieves small approximation errors in simulations

Demonstrates computational efficiency in quadcopter example

Effective for systems with rapid changes

Abstract

This paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which is resulted from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach.