This paper proposes a sensor-reduction control in order to control the output voltage of the dual active bridge (DAB) converter under dual-phase-shift (DPS) modulation. The deadbeat control-based Lagrange multiplier method (LMM) is adopted to achieve current stress optimization (CSO). A first-order extended state observer (ESO) is established to observe the load current based on the basis of the dynamic equation of the output capacitor. Compared to the existing ESO for the DAB converter, the proposed observer is able to reject disturbances even when output capacitor mismatches occur, resulting in better observer performance. Besides, the proposed method exhibits good steady-state performance without using any compensating controller. Consequently, the proposed method enables current sensorless control and significantly decreases the number of control parameters, resulting in increased simplicity and cost-saving. The simulation and experimental results obtained with a 300 W prototype demonstrate that the proposed method outperforms the existing methods under changing load current and input voltage conditions.INDEX TERMS Dual active bridge, current sensorless, dual-phase-shift, extended state observer, parameter mismatch.