A Comparison between Markov Chain and Koopman Operator Based Data-Driven Modeling of Dynamical Systems

TL;DR

This paper compares Markov chain and Koopman operator methods for data-driven modeling of dynamical systems, highlighting their similarities, differences, and performance in autonomous and controlled scenarios.

Contribution

It clarifies the similarities between the two frameworks and introduces their models and control methods, providing a comprehensive comparison.

Findings

Both models show comparable accuracy for autonomous systems.

Koopman models are more computationally efficient in certain cases.

Differences emerge when modeling systems with control inputs.

Abstract

Markov chain-based modeling and Koopman operator-based modeling are two popular frameworks for data-driven modeling of dynamical systems. They share notable similarities from a computational and practitioner's perspective, especially for modeling autonomous systems. The first part of this paper aims to elucidate these similarities. For modeling systems with control inputs, the models produced by the two approaches differ. The second part of this paper introduces these models and their corresponding control design methods. We illustrate the two approaches and compare them in terms of model accuracy and computational efficiency for both autonomous and controlled systems in numerical examples.