Fixed-time formation-containment control for uncertain multi-agent systems with varying gain extended state observer

In this article, the fixed-time formation-containment control is investigated for multi-agent systems with model uncertainties and external disturbances . First, a novel fixed-time varying gain extended state observer is developed to observe the states and the total disturbance of each formation-leader and follower. Then a fixed-time formation control protocol for each formation-leader is constructed to realize formation tracking. The desired trajectory for the formation-leader is generated by a fixed-time formation distributed observer. It can estimate the information of the tracking-leader within fixed time. Furthermore, a fixed-time containment distributed observer is put forward for each follower to estimate the convex hull spanned by the states of the formation-leaders, which can generate the reference signal for each follower and thus a fixed-time containment control protocol can be developed. Finally, the proposed strategy is successfully applied to the wheeled mobile robots . Experimental results confirm the validity of the proposed approach.