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In this paper, a data-driven predictive controller is designed for the start-up process of vehicles with automated manual transmissions (AMTs). It is obtained directly from the input-output data of a driveline simulation model constructed by the commercial software AMESim. In order to obtain offset-free control for the reference input, the predictor equation is gained with incremental inputs and outputs. Because of the physical characteristics, the input and output constraints are considered explicitly in the problem formulation. The contradictory requirements of less friction losses and less driveline shock are included in the objective function. The designed controller is tested under nominal conditions and changed conditions. The simulation results show that, during the start-up process, the AMT clutch with the proposed controller works very well, and the process meets the control objectives: fast clutch lockup time, small friction losses, and the preservation of driver comfort, i.e., smooth acceleration of the vehicle. At the same time, the closed-loop system has the ability to reject uncertainties, such as the vehicle mass and road grade.