When operated under single-phase shift (SPS) modulation, the dual-active bridge (DAB) DC-DC converter, a popular topology for isolated power conversion, has significant issues. In particular, the converter experiences large backflow power and reduction in the zero-voltage switching (ZVS) region under light load or when the voltage ratio deviates from unity. These operational inefficiencies compromise the overall efficiency and increase conduction losses in the high-frequency transformer, switching losses, and switch stress. This paper proposes an optimal control strategy (OCS) based on the Karush-Kuhn-Tucker (KKT) optimization to minimize the backflow power and extend the ZVS range. A comprehensive mathematical analysis of various modes, including the derivation of mathematical models for transmission power, backflow power, and ZVS conditions. Finally, an experimental prototype of the DAB converter was built in the lab, and the performance of the proposed control strategy was validated using experimental and comparison results.