The energy management of a hybrid fuel cell / supercapacitor system is studied, both in simulation and on a test bench, for experimental validation. This system can be used to power a urban electric scooter. Two off-line energy management strategies are implemented and compared to control the power split between the fuel cell and the supercapacitor: Pontryaguine minimum principle (PMP) and dynamic programming. In the case of PMP, time evolution of the co-state is accounted for, and operational constraints on the supercapacitor state of charge are included. Simulation and experimental results agree very well, which validates the system model and the implementation of the control strategies on the real system. This work will be used as a basis to develop online strategies.