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Fuel cells represent an area of great industrial interest due to the possibility to generate clean energy for stationary and automotive applications. It is clear that the proper performance of these devices is closely related to the kind of control that is used; therefore, a study of improved control alternatives is fully justified. The air-supply control is widely used to guarantee safety and to achieve a high performance. This paper deals with this control loop, proposing and comparing two control objectives aimed at satisfying the oxygen starvation avoidance criterion and the maximum efficiency criterion, respectively. The control architecture is based on a constrained explicit model predictive control (MPC) law suitable for real-time implementation due to its low computational demands. The proposed controller is implemented and evaluated on a 1.2-kW polymer electrolyte membrane or proton exchange membrane fuel-cell test bench, thus obtaining real data which show that the maximum efficiency criterion does not conflict with the starvation avoidance criterion and allows system performance improvements of up to 3.46%. Moreover, experimental results utilizing the explicit MPC approach also show improved transient responses compared to those of the manufacturer's control law.