Robust constraint satisfaction and stability of virtually coupled train set with uncertain dynamics: A dual-mode robust MPC approach

Abstract

As a hot topic in railways, virtual coupling technology connects multiple trains (units) as a virtually coupled train set (VCTS) and aims to improve the performance of train operation by keeping a small following distance between successive units. For the desired performance, robust constraint satisfaction and stability are crucial properties of a VCTS. However, they are hard to be simultaneously guaranteed with uncertain train dynamics. To solve this problem, we propose a dual-mode robust model predictive control (DRMPC) approach. First, by considering uncertain actuator gains and resistance parameters, the VCTS operation is modeled with safety and input constraints. Then, we put forward a dual-mode scheme to adopt a controller from two candidates. Among this, we formulate a feedback controller through the analysis of local and string stability and adopt it in an admissible region to efficiently guarantee the crucial properties. To handle the rest cases with the risk of constraint dissatisfaction, an optimal controller is yielded by solving a constrained optimization framework employing the homothetic-tube technique. Specifically, local tubes are recursively constructed online by the set-membership prediction, while considering the tubes from the preceding unit. Next, the robust constraint satisfaction and stability of the VCTS are proved within the closed-loop implementation of DRMPC. Finally, experimental results verify the performance and advantages of the proposed approach on a VCTS.