Extended Koopman Models

TL;DR

This paper proposes two advanced Koopman-based models that enhance nonlinear dynamic system prediction and control, leveraging convex dynamics and invertible control transformations, with deep learning architectures demonstrating superior performance.

Contribution

Introduces Convex and Extended Koopman Models with deep learning, improving nonlinear system prediction and control capabilities over traditional Koopman methods.

Findings

Significantly outperforms traditional Koopman models in trajectory prediction

Uses convex dynamics in lifted space for better modeling

Employs invertible control transformations for improved accuracy

Abstract

We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the potential for fast, globally optimal control of nonlinear, nonconvex systems. The first generalization, Convex Koopman Models, uses convex rather than linear dynamics in the lifted space. The second, Extended Koopman Models, additionally introduces an invertible transformation of the control signal which contributes to the lifted convex dynamics. We describe a deep learning architecture for parameterizing these classes of models, and show experimentally that each significantly outperforms traditional Koopman models in trajectory prediction for two nonlinear, nonconvex dynamic systems.