Optimal trajectory control of flexible two-link manipulator based on PDE model

This paper studies optimal trajectory control of a flexible two-link manipulator based on the partial differential equation (PDE) dynamic model. To avoid deriving optimal control directly from the cost function, which is difficult for PDE systems, we design the optimal boundary control in two steps. First, the differential evolution algorithm is applied to generate the optimal trajectory that minimizes the total energy consumption. Then, a boundary control scheme is proposed to regulate the joints along the optimal trajectories and suppress vibration simultaneously. The effectiveness of the proposed control is validated via simulations.