Abstract: In order to improve the efficiency of dual active bridge (DAB) DC-DC converter and reduce its control complexity, a closed-loop optimal control strategy for minimum current stress based on the extended-phase-shift control method is proposed. Firstly, according to the phase relationship between the output voltages of the full bridge on both sides and the magnitude of the phase shift angle in the bridge, the phase shift ratio of extended-phase-shift control is redefined to ensure the positive correlation between the phase shift ratio and the transmission power. Then, the operating modes of DAB are divided based on the on-off sequences of the active switch, and two of them are selected as the actual operating modes. Moreover, the Karush-Kuhn-Tucker condition method is adopted to optimize the current stress in the whole load range under the condition of soft switching, and a more concise closed-loop optimization control strategy is designed based on the combination with the proposed phase shift ratio. Finally, the DAB simulation model and experimental prototype are both established to verify the proposed control strategy. The results show that the proposed control strategy not only has the advantages of simple and easy-implementation, but also can realize the minimum current stress control and the soft switching characteristics of the active switch within the whole load range.