In this paper, a bidirectional DC/DC converter with two voltage source at both ends operating in both discontinuous conduction mode (DCM) and continuous conduction mode (CCM) is discussed. The average model for each topology, i.e., buck, boost, and buck–boost, is derived. Due to the contradictory nature of DCM and CCM, conventional controllers fail to achieve smooth transition while crossing between these modes. Two adaptive fuzzy logic controllers (FLC) incorporated into a local model network (LMN) are proposed to achieve accurate and smooth control of the converter in both DCM and CCM. The proposed control scheme does not require any a priori offline training, weights initialization, and parameters knowledge. The adaptive fuzzy logic control strategy is compared against its proportional integral (PI) control counterpart, and their performance is verified under parameter variations.