Polynomial trajectory tracking of networked Euler-Lagrange systems

The coordinated tracking problem of networked Euler-Lagrange systems is studied in this paper. According to the knowledge of classical control, an integral term can eliminate the steady-state error when solving the tracking problem. A proportional-integral-derivative (PID) tracking protocol is then first proposed to solve the tracking problem of Euler-Lagrange systems where the leader has a quadratic trajectory. By properly choosing parameters, it is proved that all followers can asymptotically track the leader´s quadratic trajectory if the communication topology graph has a spanning tree. Furthermore, a so-called PI^mD tracking protocol is derived by adding some high-order integral terms. It is shown that this PI^mD tracking protocol can solve the tracking problem of networked Euler-Lagrange systems with a leader having the higher-order polynomial trajectory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed protocol.