The multi-agent formation of leader-follower pattern may not complete the task due to the communication failure caused by the local fault of the leader system. To solve this problem, this paper proposes a distributed adaptive control approach based on the consensus theory. The controlled object consists of four agents forming a triangle formation system, with the vertex of the triangle acts as the leaders, and the remaining agents act as followers. In addition, the speed direction of the leader is the forward direction of the formation, and the followers are behind the leader. Based on the graph theory, the distributed adaptive updating of the agent’s local information parameters are carried out, and the distributed adaptive control law is used to supplement the influence of the leader’s fault in the multi-agent formation. Based on the local information of adjacent agents, the overall distributed adaptive fault-tolerant control law is designed, and the stability of the designed controller is proved by constructing the Lyapunov function. Meanwhile, the relative distance error between the horizontal direction and longitudinal direction of the "leader-follower" converge to a fixed constant. The simulation results show that the proposed adaptive control approach has good robustness, which provides a theoretical basis for the engineering practice.
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