Koopman-based NMPC reduces computation for virtual train coupling

A team led by Yiwen Zhang from multiple institutions has introduced a Koopman-based nonlinear model predictive control (K-NMPC) framework for virtually coupled train systems — a concept where trains operate in tight, coordinated packs without physical coupling. The method addresses a key bottleneck: the computational expense of optimal control for real-time train tracking. By systematically lifting the nonlinear train dynamics (including speed limits, passenger comfort constraints, and collision avoidance) into a finite-dimensional Koopman space via closed-form observable functions, the system transforms the online control problem into a simple quadratic program. This analytic approach avoids the iterative optimization typical of traditional nonlinear MPC, drastically cutting per-step computation.

Benchmarked against a time-discrete NMPC scheme, the K-NMPC delivers comparable control performance — in tracking accuracy, constraint satisfaction, and passenger comfort — while requiring significantly less online computation time. The authors highlight the method's strong potential for real-time deployment in practical virtually coupled train control systems, where low latency is critical for safe coordination at high speeds and tight headways. The work is set to be presented at the IFAC World Congress 2026.