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In this paper, a torque-demand-based control approach is developed for parallel hybrid powertrains that consist of a torque distributor, a load observer, and two feedback control loops for an internal combustion engine and an electric motor, respectively. The torque distributor is composed of the torque demand, torque split, torque compensation, and torque limit. The torque control law for the engine is constructed with model predictive control based on a nonlinear mean-value model. A proportional-integral (PI) observer is designed to estimate the torque load of the powertrain, which is Lyapunov stable. For the electric motor, a linear model predictive control law is designed with current feedback. To validate the proposed torque demand control approach, simulation results that were conducted on a simulator are demonstrated, in which full-scaled dynamics of the powertrain are simulated.