High-speed magnetic levitation (Maglev) vehicles have the potential to close the existing gap between classical railroads and air travel. However, efforts in the high-speed sector have stopped in the meantime, but now Maglev technology is experiencing a renaissance in China. The latter accompanies with the intention to reach a maximum speed of 600 km/h, which, however, immediately increases the demands on the magnet control system. As less attention was paid to this technology in the meantime, the research in methods for controlling the unstable magnet system almost stagnated. At the same time, the optimization-based control methodology model predictive control (MPC) evolved toward an efficient control technique. Against this background, the dissertation at hand thoroughly combines the topics of MPC and high-speed Maglev vehicles and, in particular, deals with the issue of whether a practical realization seems possible. First, this includes deriving mathematical models, which the MPC internally uses to predict the expected actual system behavior. In addition, the treatise provides a valuable contribution to the design of practically applicable offset-free MPC control structures. Furthermore, real-time capable MPC algorithms are tested in realistic Processor-in-the-Loop and Hardware-in-the-Loop setups, revealing that the MPC's real-time dilemma can be overcome. The work also contributes in the context of dependable control architectures to safeguard the derived practically stable and efficient MPC-based control laws. The final control concept's application within detailed vehicle simulation models shows the MPC's advantages and capabilities as a holistic, efficient, powerful, and real-time capable control approach, which has the potential to meet future requirements.