Data-Driven Modeling and Control for Lane Keeping System of Automated Driving Vehicles: Koopman Operator Approach

Abstract

This paper proposes the data-driven modeling and control method with the Koopman operator for the lane-keeping system. The vehicle can be modeled as a linear motion model but has underlying complicated nonlinear behavior. Thus, there exists a need to model the full vehicle dynamics effectively. To this end, we use the Koopman operator to express the full vehicle nonlinear dynamics as a linear structure. However, it is not practical to use the Koopman operator directly because it lies in infinite-dimensional space. Hence, we apply the extended dynamic mode decomposition to approximate the Koopman operator as a finite-dimensional linear operator. We conduct a comparative study between the linear model-based optimal control and the Koopman operator-based optimal control. As a result, it is observed that the proposed method reduces the system state by 20% compared to the linear model-based controller.