Koopman Operator-based Model Identification and Control for Automated Driving Vehicle

Abstract

This paper proposes the Koopman operator-based model identification and control method for a lane-keeping system. The Koopman operator is a linear mapping that can capture nonlinear dynamics but lies in an infinite-dimensional space. Thus, we adopted the extended dynamic mode decomposition (EDMD) to approximate the Koopman operator in a finite-dimensional space. Then, we designed a linear structure to express the nonlinear motion of full vehicle dynamics using the advantage of the Koopman approach. In the Koopman operator-based model identification, selecting the basis function for lifting the state is crucial, but how systematically to choose the basis functions is an open problem. Thus, in this study, we made a comparative study among the typical basis functions. In addition, we applied signal normalization to mitigate the potential problem of the EDMD approach. Furthermore, this paper used the approximated Koopman operator to design the optimal control as a linear structure for the underlying nonlinear vehicle model. Finally, we confirmed that the closed-loop system is uniformly ultimately bounded with the proposed controller. A full vehicle dynamic simulator, CarSim, obtains the data for calculating the Koopman operator. The comparative study confirmed that the position error of the proposed method was reduced by 36% compared with other methods.