This paper presents a Hamiltonian/differential flatness control law designed for the management of fuel cell/supercapacitor hybrid systems in DC microgrid applications. The control strategy aims to optimize energy management while enhancing the efficiency and stability of DC microgrids. By leveraging the complementary characteristics of fuel cells (high energy density, slow dynamics) and supercapacitors (high power density, rapid response), it addresses specific limitations. The energy of the systems is governed by the Hamiltonian framework, while the differential flatness theory enables precise control of system dynamics, ensuring optimal operation and accurate trajectory tracking. To assess the performance of the control algorithm, an experimental test bench has been established. Experimental results confirm the effectiveness of the control law in managing a load-drive cycle under constant power load conditions, balancing power flow, reducing fuel cell stress, and extending the life of the supercapacitor.