By taking an automatic transmission that implements the power shifting only with a single friction clutch as the research objective,the dynamic process of positive-torque downshifting of automatic transmission is analyzed to establish a coordination control strategy for friction clutch and engine torque.By considering the jerk at the end of the inertia phase and the friction work as the comprehensive objective functional,the coordination control is ac- complished on the basis of minimum principle,which is used to optimize the inertia phase in downshifting process with torque constraints.Moreover,by taking the gradient of the power source torque and the friction clutch as two control variables and by applying the inequality constraints on control variables and state variables,the constrained Bolza problem is solved numerically and the optimal state variables’trajectory is obtained.Simulation and bench test results indicate that the proposed method effectively decreases the torque fluctuation of transmission output shaft,promotes the dynamic property and improves the shift quality.