A Comparison of the Effects of One-Step Integration Methods on Nonlinear MPC-Based Controllers for Trajectory Tracking

Model predictive control (MPC) has been widely used in a wide range of industrial fields. How to balance the accuracy and real-time of the MPC-based controllers is still a challenging problem. In terms of the controller's accuracy, most studies focus on the problem of how to improve the system model's accuracy to improve the controller's performance without considering the algorithm errors of the integration methods used to establish the prediction model. In this paper, we investigate the effects of four distinct one-step integration methods (i.e. explicit and implicit Euler method, midpoint, and Heun's method) on nonlinear MPC-based trajectory tracking controllers. These integration methods are used to establish the predictive models to build up different MPC-based trajectory tracking controllers for autonomous driving vehicles. The performance of the MPC-based controllers is tested on a double-line change path. It is demonstrated that the choices of the control horizon and integration methods affect MPC-based controllers' tracking performance. MPC-based controllers using the backward Euler method with the optimal control horizon have the best tracking performance.