Distributed Koopman NMPC for Virtually Coupled Train Control

This paper presents a distributed Koopman-based nonlinear model predictive control (NMPC) for virtually coupled train system. Considering nonlinear train dynamics and operational constraints on both states and control inputs, a nonlinear continuous-time tracking control problem is formulated for each train. An analytical observable generation procedure is employed to lift the nonlinear dynamics into the Koopman space, yielding a bilinear lifted system representation. Through bilinearity relaxation and discretization of the lifted dynamics, a linear discrete-time system is obtained, enabling nonlinear programs to be closely approximated by quadratic programs within the MPC framework. Based on a train-to-train communication topology, a distributed implementation is adopted in which each train solves a local optimization problem using updated information received from its preceding train. Simulation results demonstrate that the proposed approach achieves tracking performance comparable to that of a distributed baseline NMPC while significantly reducing computation time, thereby supporting its applicability to real-time virtually coupled train systems.