This work studies a novel low voltage (<60 V) hybrid system that supports engine boosting and downsizing in addition to start-stop, regenerative braking, and constrained torque assist/regeneration. The hybrid power split supercharger (PSS) shares a 9 kW motor between supercharging the engine or providing hybrid functionalities through a planetary gear set, a brake and a bypass valve. The PSS operation is limited to only one of the parallel hybrid or boosting modes at a time, necessitating a highly optimized decision making algorithm to select the device mode and power split ratio. In this work an adaptive equivalent consumption minimization strategy (A-ECMS) is developed for energy management of the PSS. The A-ECMS effectiveness is compared against a dynamic programming (DP) solution with full drive cycle preview through hardware-in-the-loop experiments on an engine dynamometer testbed. The experiments show that the PSS with A-ECMS reduces a vehicle fuel consumption by 18.4% over standard FTP75 cycle compared to a baseline turbocharged engine, while global optimal DP solution decreases the fuel consumption by 22.8% compared to baseline.