Random trajectory tracking of flexible manipulator with buffer

Modeling, tracking and stability analysis for flexible manipulator with buffer under stochastic disturbance is researched. In the absence of noise, the Lagrange system is obtained combining kinetic energy with potential energy. The stochastic oscillation in the environment is equivalently transformed into disturbance to the controller, and the Lagrangian system with colored noise is obtained. Based on the quasi-lower triangular structure of the model, a trajectory tracking controller with design parameters is obtained by using the multiple-input-to-multiple-output backstepping method, such that the nonlinear system is noise-to-state stable in probability. By adjusting the parameters of the design scheme, the result of tracking error is small enough as we expected.