Time-varying group formation tracking control problems for second-order multi-agent systems with communication delays and multiple leaders are addressed in this paper. The followers are divided into multiple subgroups, and each subgroup is driven to complete the time-varying sub-formation and to track the average state of entire leaders simultaneously. A distributed protocol that considers communication delays and uses only local interaction information is presented. According to Lyapunov-like stability approach, sufficient conditions for the multi-agent systems to realize time-varying group formation tracking with multiple leaders are given. A variable-substitution based method is developed to get the unknown feedback matrix of the protocol and an algorithm is given to summarize the steps to construct the protocol. The theoretical results can be used in the problem of multiple targets enclosed by several subgroups of unmanned aerial vehicles. Finally, numerical examples are applied to verify the feasibility of the proposed results.

本文研究了具有通信延迟和多个领导者的二阶多智能体系统的时变群形成跟踪控制问题。追随者分为多个子组，每个子组都被驱动以完成随时间变化的子形式并同时跟踪整个领导者的平均状态。提出了一种考虑通信延迟并仅使用本地交互信息的分布式协议。根据类Lyapunov稳定性方法，给出了多智能体系统实现多领导者时变群形成跟踪的充分条件。开发了一种基于变量替换的方法来获取协议的未知反馈矩阵，并给出了一种算法来总结构建协议的步骤。理论结果可用于无人飞行器几个子组包围的多个目标的问题。最后，通过数值算例验证了所提结果的可行性。