Fully distributed time-varying formation tracking control for linear multi-agent systems with unknown external disturbances.

This work investigates the time-varying formation tracking (TVFT) problem for linear multi-agent systems with a leader of unknown input in the presence of unknown external disturbances on directed graphs. Each agent is subjected to different external disturbances generated by unknown exosystems. To eliminate the unknown external disturbances of each follower, an adaptive disturbance observer and a state observer are constructed first. Then, utilizing the estimated information, a fully distributed TVFT protocol is designed with adaptive coupling parameters such that the global information of the communication topology is not required. By the developed distributed controller, the multi-agent system on a communication topology containing a directed spanning tree can asymptotically track the leader with a desired time-varying formation and simultaneously reject external disturbances in spite of their unknown exosystems. Furthermore, the proposed controller is modified to a continuous one to eliminate the chattering problem. Finally, a simulation example is provided to illustrate the effectiveness of theoretical results.