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Solid oxide fuel cells (SOFCs) offer a number of advantages beyond those of most other fuel cells. However, like other fuel cells, rapid load following is difficult, and can lead to fuel starvation and consequently fuel cell damage. Mitigating fuel starvation and improving load following capabilities are conflicting control objectives. However, the issue can be addressed by the hybridization of the system with an energy storage device. In this paper, a steady-state property of the SOFC, combined with a current regulation strategy, is used to manage transient fuel utilization and thereby address fuel starvation. Meanwhile, an overall system strategy is employed to manage energy sharing in the hybrid system for load following as well as for maintaining the state-of-charge of the energy storage device. This work presents an adaptive control algorithm that uses online parameter estimation to update the controller. The control design is validated on a hardware-in-the-loop setup and experimental results are provided.