A robust MPC approach with controller tuning for close following operation of virtually coupled train set

Virtual coupling, as an emerging concept in railways, expects successive trains in a virtually coupled train set (VCTS) to maintain a short following distance. However, this close following operation is still difficult to be achieved given uncertain resistances and nonlinear safety constraints. To solve this problem, this paper proposes a robust model predictive control (RMPC) approach for the close following operation of VCTS while satisfying a nonlinear safety constraint with relative braking principle. First, we construct a robust positively invariant set that bounds the tracking errors caused by uncertain resistances. Further, a semi-definite program-based controller tuning algorithm is proposed to reduce the following distance in the premise of the tightened constraint for robustly satisfying the nonlinear safety constraint. Then, by mathematically examining the future trajectories of successive trains, we create a terminal constraint set to ensure the recursive feasibility of the proposed RMPC. This closed-loop property guarantees the satisfaction of the safety constraint in any situation, even in the case of sudden deceleration of VCTS. Finally, numerical experiments are conducted to evaluate the following distance with respect to heterogeneous trains and verify the effectiveness of our approach. Experimental results demonstrate that the expected close following operation can be achieved while robustly satisfying the nonlinear safety constraint with uncertain resistances. Moreover, our approach further reduces the following distance in a VCTS by over 5%, compared with existing research.