Distributed MPC for Virtually Coupled Train Set Subject to Safety Constraints With Communication Delays

This paper presents a distributed model predictive control (DMPC) approach for a virtually coupled train set (VCTS) with communication delays. Specifically, we stabilize the real-time states of VCTS and guarantee the satisfaction of safety constraints in automatic train protection systems with delayed states, which fills the gap in the existing literature. First, using the predicted trajectories at previous instants, the real-time states of VCTS are estimated from delayed states obtained through communication. Then, compatibility constraints are designed to regulate predicted control inputs, such that the error between the predicted and actual trajectories in the prediction horizon can be confined in a sequence of sets. Next, linear matrix inequalities are derived to tune cost functions, terminal sets and terminal controllers, which guarantee the stability and recursive feasibility of DMPC. Finally, experimental results demonstrate the performance of our approach in both cruising and speed-varying operations. The minimal spacing policies are evaluated with different communication delays and parameters in DMPC based on our mathematical designs.