On Gaussian Process Based Koopman Operators

Model-Based Control Using Koopman Operators

This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting modelbased control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-dri...

Weighted Frobenius-Perron and Koopman operators

2 Summarized theory of Koopman operators

Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman operator itself is linear but infinite-dimensional (evolves on a function space). This linear operator captures the full information of the dynamics described b...

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Fault Detection Based on Gaussian Process Models

The traditional model-based fault detection and isolation (FDI) rely on tacit assumption that the validity of process model is out of question for current process data. However, it happens in practice that a process might end up in regions for which the underlying model is not validated. This can result in false alarms. To avoid the risk, a validity index is suggested as a measure of confidence...