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A power-split hybrid electric vehicle (HEV) combines the advantages of both series and parallel hybrid vehicle architectures by utilizing a planetary gear set to split and combine the power produced by electric machines and a combustion engine. Because of the different modes of operation, devising a near optimal energy management strategy is quite challenging and essential for these vehicles. To improve the fuel economy of a power-split HEV, we first formulate the energy management problem as a nonlinear and constrained optimal control problem. Then two different cost functions are defined and model predictive control (MPC) strategies are utilized to obtain the power split between the combustion engine and electrical machines and the system operating points at each sample time. Simulation results on a closed-loop high-fidelity model of a power-split HEV over multiple standard drive cycles and with different controllers are presented. The results of a nonlinear MPC strategy show a noticeable improvement in fuel economy with respect to those of an available controller in the commercial Powertrain System Analysis Toolkit (PSAT) software and the other proposed methodology by the authors based on a linear time-varying MPC.