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This paper introduces a dynamic model of the driver control strategy of lane-change behavior and applies it to trajectory planning in driver-assistance systems. The proposed model reflects the driver control strategies of adjusting longitudinal and latitudinal acceleration during the lane-change process and can represent different driving styles (such as slow and careful, as well as sudden and aggressive) by using different model parameters. We also analyze the features of the dynamic model and present the methods for computing the maximum latitudinal position and arrival time. Furthermore, we put forward an extended dynamic model to represent evasive lane-change behavior. Compared with the fifth-order polynomial lane-change model, the dynamic models fit actual lane-change trajectories better and can generate more accurate lane-change trajectories. We apply the dynamic models in emulating different lane-change strategies and planning lane-change trajectories for collision prediction. In the simulation, we use the models to compute the percentage of safe trajectories in different scenarios. The simulation shows that the maximum latitudinal position and arrival time of the generated lane-change trajectories can be good indicators of safe lane-change trajectories. In the field test, the dynamic models can generate the feasible lane-change trajectories and efficiently obtain the percentage of safe trajectories by computing the minimum gap and time to collision. The proposed dynamic model and module can be combined with the human-machine interface to help the driver easily identify safe lane-change trajectories and area.