Distributed Tracking of a Class of Underactuated Lagrangian Systems With Uncertain Parameters and Actuator Faults

A distributed adaptive controller is proposed in this paper for a class of underactuated Lagrangian systems to control the actuated variables to track a dynamic leader and keep unactuated ones bounded under a directed communication graph. A finite-time observer is introduced to estimate the leader's velocity. Based on two sliding variables defined for the actuated and unactuated channels, adaptive controllers are designed for the underactuated Lagrangian systems subject to uncertain parameters and external disturbances without or with actuator faults. The convergences of the proposed controllers are proven based on the separation principle between the observer and the controller. Finally, simulations and experiments are conducted to verify the effectiveness of the proposed controllers.