Propagation of Uncertainty with the Koopman Operator

Servadio, Simone; Lavezzi, Giovanni; Hofmann, Christian; Wu, Di; Linares, Richard

Propagation of Uncertainty with the Koopman Operator

File

2024-Servadio-PropagationOfUncertainty.pdf (1.13 MB)

Date

2024-07-29

Authors

Servadio, Simone

Lavezzi, Giovanni

Hofmann, Christian

Wu, Di

Linares, Richard

Abstract

This paper proposes a new method to propagate uncertainties undergoing nonlinear dynamics using the Koopman Operator (KO). Probability density functions are propagated directly using the Koopman approximation of the solution flow of the system, where the dynamics have been projected on a well-defined set of basis functions. The prediction technique is derived following both the analytical (Galerkin) and numerical (EDMD) derivation of the KO, and a least square reduction algorithm assures the recursivity of the proposed methodology.

Academic or Administrative Unit

Department of Aerospace Engineering

Type

Preprint

Comments

This is a preprint from Servadio, Simone, Giovanni Lavezzi, Christian Hofmann, Di Wu, and Richard Linares. "Propagation of Uncertainty with the Koopman Operator." arXiv preprint arXiv:2407.20170 (2024). doi: https://doi.org/10.48550/arXiv.2407.20170.

Rights Statement

https://creativecommons.org/publicdomain/zero/1.0/