To improve the shift quality of dual clutch transmission (DCT) vehicles and reduce the jerk and sliding friction in the shift process, a real-time planning of clutch optimal engagement trajectory and control method in the shift process is proposed. This method combines pseudo-spectral optimization, machine learning, and model predictive control. First, considering the jerk, sliding friction work, and shift time as the optimization indices, the adaptive pseudo-spectral method is employed to optimize the engagement trajectory of the clutch during the shift process. Based on the optimal trajectory data set, a gradient boosting decision tree-based real-time planning method for the clutch target engagement trajectory is proposed. Second, a model predictive control strategy for the shift process is proposed based on the DCT system model to track the optimal target trajectory in real-time. Simulations and experiments reveal that the proposed target engagement trajectory planning method can plan the clutch target engagement trajectory for various accelerator pedal openings and initial clutch speed states in real-time, and the proposed model predictive control method can accurately track the target trajectory. Compared with the original vehicle strategy, under 35% and 65% accelerator pedal opening, the maximum absolute value of jerk produced by the proposed strategy was reduced by 31.06% and 31.46%, respectively, and the sliding friction work was reduced by 22.87% and 23.24%, respectively. The shift times of the proposed strategy under 35% and 65% accelerator pedal openings were 19.12% and 20.69% lower than that of the original vehicle strategy, respectively.