# Data-driven identification of vehicle dynamics using Koopman operator

## TL;DR

This paper explores vehicle dynamics identification using the Koopman operator, transforming nonlinear systems into linear ones in higher-dimensional spaces through basis functions, with two approaches for basis selection demonstrated.

## Contribution

It introduces two novel methods for selecting basis functions in Koopman operator-based vehicle dynamics modeling, including a data-driven approach and one leveraging known nonlinear dynamics.

## Key findings

- Both approaches successfully model vehicle dynamics.
- Eigenfunction-based basis functions improve prediction accuracy.
- Discussion on basis function selection enhances Koopman operator application.

## Abstract

This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis functions, where the system dynamics is linear. The selection of basis functions is crucial and there is no general approach on how to select them, this paper gives some discussion on this topic. Two distinct approaches for selecting the basis functions are presented. The first approach, based on Extended Dynamic Mode Decomposition, relies heavily on expert basis selection and is completely data-driven. The second approach utilizes the knowledge of the nonlinear dynamics, which is used to construct eigenfunctions of the Koopman operator which are known by definition to evolve linearly along the nonlinear system trajectory. The eigenfunctions are then used as basis functions for prediction. Each approach is presented with a numerical example and discussion on the feasibility of the approach for a nonlinear