针对"领航者-跟随者"的多智能体编队，由于领航者系统出现故障引起编队通讯中断而不能完成任务的问题，提出了一种基于一致性理论的分布式自适应控制方法，用于解决该问题。首先，以一个位于顶点的智能体作为领航者，其余3个位于同一条线上的智能体作为跟随者，由此所构成的三角形编队作为被控对象。其中，领航者速度方向作为编队的前行方向，跟随者位于领航者之后。其次，基于图论，对智能体局部信息参数进行分布式自适应更新，并设计分布式自适应控制律，用于弥补多智能体编队中领航者故障所造成的影响。同时，根据相邻智能体的局部信息，设计整体分布式自适应容错控制律，进一步通过构建合理的Lyapunov函数，证明所设计控制器的稳定性，以及"领航者-跟随者"之间相对横向以及相对纵向的距离误差均收敛于固定常数。最后，仿真验证表明：所提出的自适应控制方法具有良好的鲁棒性，这也为工程实践提供了理论依据。
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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