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This paper presents a methodology of calculating the optimal torque and speed commands for the engine-generator system of a series hybrid electric vehicle (HEV). In series HEVs, the engine-generator subsystem provides electrical energy to the dc link. This paper proposes an optimal control strategy of the engine-generator subsystem to generate a desired amount of energy within a given period of time. The optimization algorithm, based on trajectory optimization, determines the torque and speed reference signals for the engine-generator subsystem that achieve maximum efficiency. A simplified version of the controller is also presented for online implementation. The proposed control strategy is compared with nonoptimized control techniques, and simulation results show the improvements in energy efficiency.