In order to improve the shift quality,a linear quadratic optimal tracking control algorithm for automatic transmission shift process is proposed.The dynamic equations of the shift process are derived using a Lagrange method.And a powertrain model is built in the Matlab/Simulink and verified by the measurements.Considering the shift jerk and friction loss during the shift process,the tracking trajectories of the turbine speed and output shaft speed are defined.Furthermore,the linear quadratic optimal tracking control performance index is proposed.Based on the Pontryagin’s minimum principle,the optimal control law of the shift process is presented.Finally,the simulation study of the 1-2 upshift process under different load conditions is carried out with the powertrain model.The simulation results demonstrate that the shift jerk and friction loss can be significantly reduced by applying the proposed optimal tracking control method. In order to improve the shift quality, a linear quadratic optimal tracking control algorithm for automatic transmission shift process is proposed. The dynamic equations of the shift process are derived using a Lagrange method. And a powertrain model is built in the Matlab / Simulink and verified by the measurements. Cautionring the shift jerk and friction loss during the shift process, the tracking trajectories of the turbine speed and output shaft speed are defined. Morerther, the linear quadratic optimal tracking control performance index is proposed. Based on the Pontryagin’s minimum principle, the optimal control law of the shift process is presented. Finally, the simulation study of the 1-2 upshift process under different load conditions is carried out with the powertrain model. The simulation results demonstrate that the shift jerk and friction loss can be significantly reduced by applying the proposed optimal tracking control method.