The present thesis aims at evaluating the advantages of the transformation of a conventional heavy-duty vehicle featured by a 4.5L diesel engine into a full hybrid version by applying an Adaptive - Equivalent Consumption Minimization Strategy (A-ECMS). A p2 parallel hybrid configuration has been simulated in a design optimization tool. The controller has been integrated within the simulation environment under multiple formulations, either extracted from the literature or proposed in innovative solutions. Simulations have been carried out in MATLAB and validated by comparing the results obtained by the Dynamic Programming optimization algorithm. In order to understand the behaviour of the vehicle in multiple traffic scenarios, WHVC (Worldwide Harmonized Vehicle Cycle), FTP-72 (Federal Test Procedure) and JC08 (Japan Cycle 08) have been used as driving cycles for the testing campaign..