Analysis of Truncated Singular Value Decomposition for Koopman Operator-Based Lane Change Model

TL;DR

This paper evaluates the effectiveness of truncated SVD in approximating Koopman operators for lane change modeling, highlighting limitations in computational efficiency and information retention.

Contribution

It provides a comparative analysis of basis functions and SVD ranks in EDMD for lane change models, revealing limitations of truncated SVD.

Findings

Truncated SVD does not significantly reduce training time.

Truncated SVD causes notable information loss.

Basis function choice impacts model accuracy.

Abstract

Understanding and modeling complex dynamic systems is crucial for enhancing vehicle performance and safety, especially in the context of autonomous driving. Recently, popular methods such as Koopman operators and their approximators, known as Extended Dynamic Mode Decomposition (EDMD), have emerged for their effectiveness in transforming strongly nonlinear system behavior into linear representations. This allows them to be integrated with conventional linear controllers. To achieve this, Singular Value Decomposition (SVD), specifically truncated SVD, is employed to approximate Koopman operators from extensive datasets efficiently. This study evaluates different basis functions used in EDMD and ranks for truncated SVD for representing lane change behavior models, aiming to balance computational efficiency with information loss. The findings, however, suggest that the technique of truncated SVD does not necessarily achieve substantial reductions in computational training time and results in significant information loss.