Analysis of Truncated Singular Value Decomposition for Koopman Operator-Based Lane Change Model
This is an incremental analysis for autonomous driving researchers, focusing on computational efficiency in dynamic system modeling.
The study tackled the problem of modeling lane change behavior for autonomous driving using truncated SVD with Koopman operators, finding that it did not significantly reduce computational training time and caused substantial information loss.
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.