To better solve the problem of clutch engagement process caused by variability of the clutch engagement trajectory and the tracking deviation under uncertain factors such as system parameter perturbation and external load disturbance

the optimization and tracking control method of the clutch engagement trajectory are proposed. Taking the clutch engagement process in the heavy-duty reverse shifting of the loader V-type working condition as the research object

a quadratic performance index function combining the jerk and friction work is established. Under the non-stationary random term with parameterized expression in the disturbance matrix

the variable torque optimal trajectory under the time-varying optimal control law and weight coefficient adjustment is obtained by constructing the Hamiltonian function and solving the Riccati differential equation based on Pontryagin maximum principle. To improve the tracking accuracy of the optimal trajectory under perturbation of nonlinear characteristic actuator

the quality optimization problem of the engagement process is transformed into a single target problem of trajectory tracking. The controller designed by sliding mode control method with exponential approach law achieves accurate tracking with tracking error within 0.3%

and its stability analysis is carried out by Lyapunov theory. The numerical simulation results show that the control method achieves the minimization of the friction work under the condition that the clutch engagement impact is lower than the national standard. The control method proposed in the paper will be beneficial to improve the quality of the clutch engagement process and have theoretical engineering reference value for solving similar problems.