The shifting process of a hybrid electric vehicle (HEV) could be implemented by a motor to simplify the control requirement when the clutch is engaged. In order to reduce the vehicle jerk and simplify the clutch control requirement during the shifting process, this paper introduces a 3-speed dedicated hybrid transmission (3DHT) with P1/P3 configuration and a power shift control strategy. A finite-time linear quadratic regulator (LQR) is proposed to smoothly transfer torque and suppress driveline oscillations during the torque transfer process with a maximum jerk of 5.6 m/s 3 . Since the clutch stays engaged, a predictive sliding mode control (SMC) is proposed to track the speed of the sleeve quickly and precisely during the synchronization process, which takes 0.18s and maintains a speed difference of around 1 rpm. Furthermore, a Kalman Filter is utilized to overcome the difficulties associated with side shaft torque measurement and low wheel speed resolution. A simulation is performed in MATLAB/SIMULINK, and the powershift (2nd -> 3rd) is compared with other methods. The comparison indicates that the proposed power shift strategy can reduce the maximum jerk from 14.8 m/s3 to 5.6 m/s3, while the entire shifting process lasts for 0.71s. Therefore, the proposed power shift control strategy effectively improves the shift quality.INDEX TERMS hybrid electric vehicle, power shift, dedicated hybrid transmission, linear quadratic regulator, sliding mode control