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

arXiv: https://arxiv.org/abs/2409.18586 · HTML: https://mlsanity.com/paper/2409.18586/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 27 Sep 2024.

## Builds on (most cited first, 6 of 6)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Deep Learning of Koopman Representation for Control](https://mlsanity.com/paper/2010.07546/) (2020)
- [Koopman-based lifting techniques for nonlinear systems identification](https://mlsanity.com/paper/1709.02003/) (2017)
- [Model-Based Control Using Koopman Operators](https://mlsanity.com/paper/1709.01568/) (2017)
- [Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehicles](https://mlsanity.com/paper/2007.02219/) (2020)
- [Vehicular Applications of Koopman Operator Theory -- A Survey](https://mlsanity.com/paper/2303.10471/) (2023)

## Abstract (arXiv)

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.