Ultracapacitor (UC) based ride through systems are utilized to supplement the batteries in systems such as electric/hybrid electric vehicles and islanded micro grids. The control of such a system during its discharging mode is typically performed using an outer voltage and inner current loop structure. It is desirable to have a control structure that accommodates system characteristics variations due to the deep discharge of UC stack voltage. This paper proposes an adaptive control where the control gain parameters for outer voltage loop is obtained on-line in an UC based bidirectional dc-dc converter. In this context, the disadvantage of using a fixed controller gain parameters for voltage loop is presented. The proposed control also accommodates the effect of Right Hand Plane Zero (RHZ) on the voltage loop design which affects the control bandwidth especially during deep discharges. The adaptive control not only adjusts the bandwidth of the voltage loop according to the RHZ location, but also ensures best performance possible. As a proof of concept, the proposed control is verified on a experimental setup with power level P o =120W, voltage level V g =26V with the dc-dc converter switching at f sw =100kHz.