  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
