以单摩擦元件搭接控制动力换挡式自动变速器为例，分析了自动变速器正转矩降挡动力学过程，制定了摩擦元件与动力源转矩间的协调控制策略． 以滑摩功与惯性相结束了时刻点的冲击度构造目标泛函，基于极小值原理对动力源转矩受限条件下的降挡过程惯性相进行协调控制优化． 以动力源、摩擦元件转矩变化率为双控制变量，引入状态变量、控制变量的不等式约束条件，通过对该带约束条件波尔扎问题的数值求解确定惯性相最优状态变量轨迹曲线． 仿真与台架试验结果表明，该方法有效减小了变速器输出轴的转矩波动，提升了动力性，改善了换挡品质．

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.