This paper presents a new model reference adaptive-based control (MRAC) for a single-phase shift-modulated dual active bridge DC-DC converter (SPS-DAB) with constant power loading (CPL). The non-linear control algorithm, developed based on the reduced order model of the converter, is subjected to a thorough stability and convergence analysis. The efficacy of the proposed control strategy is verified through simulations conducted on MATLAB R2023a and PLECS 4.5.6, demonstrating its capability to counteract the destabilising effects of the CPL, while ensuring precise tracking of the dual active bridge (DAB) output voltage, even amidst parameter variations. Comparative analysis highlights the superior robustness and performance of the proposed approach over the conventional proportional-integral (PI) controllers.