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The multi-stack fuel cell system (MFCS) has the advantages of higher efficiency, stronger robustness and longer life, and could be widely used in high-power application scenarios such as automobiles, airplanes, trains, and ships. The appropriate air mass flow and air pressure have a crucial impact on the output power performance indicators of the MFCS. Considering that the designed integrated air supply system for the MFCS has significant gas supply hysteresis and strong coupling between the inlet air mass flow and air pressure of each stack, this paper identifies multiple steady-state operating points of the fuel cell system to obtain corresponding linear predictive models and establishes corresponding predictive control algorithms. The Model Predictive Control (MPC) algorithms are switched in real-time based on the current load throughout the entire C-WTVC (China World Transient Vehicle Cycle) working condition.