This paper introduces an adaptive Hamiltonian energy control strategy for the proposed fuel cell hybrid power electronics architecture. The proposed controller with added integrator action is based on the Hamiltonian-Lyapunov function. In contrast to previous work, the proposed control method aims to control the output current of the fuel cell, while the DC bus voltage is controlled by the supercapacitor. Moreover, integrators are built into the control structure to eliminate steady-state errors in current and voltage, respectively. The Lyapunov candidate function is chosen to demonstrate the large-signal stability of the whole system. The experimental results demonstrate the effectiveness and feasibility of the proposed control method.