Autonomous vehicles and driving technologies have received notable attention
in the past decades. In autonomous driving systems, \textcolor{black}{the}
information of vehicle dynamics is required in most cases for designing of
motion planning and control algorithms. However, it is nontrivial for
identifying a global model of vehicle dynamics due to the existence of strong
non-linearity and uncertainty. Many efforts have resorted to machine learning
techniques for building data-driven models, but it may suffer from
interpretability and result in a complex nonlinear representation. In this
paper, we propose a deep learning framework relying on an interpretable Koopman
operator to build a data-driven predictor of the vehicle dynamics. The main
idea is to use the Koopman operator for representing the nonlinear dynamics in
a linear lifted feature space. The approach results in a global model that
integrates the dynamics in both longitudinal and lateral directions. As the
core contribution, we propose a deep learning-based extended dynamic mode
decomposition (Deep EDMD) algorithm to learn a finite approximation of the
Koopman operator. Different from other machine learning-based approaches, deep
neural networks play the role of learning feature representations for EDMD in
the framework of the Koopman operator. Simulation results in a high-fidelity
CarSim environment are reported, which show the capability of the Deep EDMD
approach in multi-step prediction of vehicle dynamics at a wide operating
range. Also, the proposed approach outperforms the EDMD method, the multi-layer
perception (MLP) method, and the Extreme Learning Machines-based EDMD
(ELM-EDMD) method in terms of modeling performance. Finally, we design a linear
MPC with Deep EDMD (DE-MPC) for realizing reference tracking and test the
controller in the CarSim environment.Comment: 12 pages, 10 figures, 1 table, and 2 algorithm