The standard model reference adaptive control (MRAC) application to the Dual Active Bridge (DAB) converter has proven to achieve excellent dynamic and tracking responses under parametric uncertainty. However, it is sensitive to bounded non-parametric uncertainty caused by measurement noise and ripples in the output voltage produced in the electronic device. When left unchecked, it affects the system's performance and may lead to instability. This paper investigates two robust modifications to the standard MRAC, namely the projection operator and dead zone techniques, to tackle the issue of the bounded noise to the dual active bridge with constant power loading (CPL). It further develops an improved form of the dead zone-based MRAC, which ensures better transient and steady-state output voltage when compared with the traditional dead-zone-based MRAC.