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The authors present the supervisory control of a parallel hybrid powertrain, focusing on several issues related to the real-time implementation of optimal control based techniques, such as the Equivalent Consumption Minimization Strategies (ECMS). Real-time implementation is introduced as an intermediate step of a complete chain of tools aimed at investigating the supervisory control problem. These tools comprise an offline optimizer based on Pontryagin Minimum Principle (PMP), a two-layer real-time control structure, and a modular engine-in-the-loop test bench. Control results are presented for a regulatory drive cycle with the aim of illustrating the benefits of optimal control in terms of fuel economy, the role of the optimization constraints dictated by drivability requirements, and the effectiveness of the feedback rule proposed for the adaptation of the equivalence factor (Lagrange multiplier).