The inherently different dynamics of a DC-DC converter while operating in both continuous conduction mode (CCM) and discontinuous conduction mode (DCM) necessitate an advanced controller to control the inductor current. A conventional PI controller cannot be used across both modes since it does not guarantee a smooth transition between both modes. Furthermore, in time-varying input-output voltage applications of the four-quadrant converter such as in battery charging applications, the location of the boundary between the CCM and the DCM changes dynamically, creating an uncertainty. Therefore, a robust controller is required to accurately track the inductor current in the presence of uncertainties. Thus, an adaptive controller is proposed in this work, which is based on the general inverse model of the four-quadrant converter in both modes. Moreover, gain scheduling is used to switch the parameters of the controller as the converter transits between the DCM and the CCM. The adaptability and effectiveness of the controller in ensuring a smooth transition is validated by numerical simulations conducted on various converter topologies. Experimental results are also presented for a buck converter.