Distributed Time-Varying Group Formation Tracking for Multiagent Systems With Switching Interaction Topologies via Adaptive Control Protocols

In this article, time-varying group formation (TVGF) tracking problems for general linear multiagent systems (GLMASs) with switching interaction topologies are investigated. Different from previous studies, a novel TVGF tracking approach is proposed, where all agents are divided into three types: the virtual leader, the group leader, and the follower. The virtual leader is designed to assign the trajectory of GLMASs. Subgroups can be interacted with each other by cooperation among group leaders such that the relative configuration between different groups can be adjusted simultaneously. The followers in each group can achieve time-varying subformations. Moreover, under the influence of external disturbances and switching topologies, based on the distributed observer, two different distributed adaptive control protocols are constructed without using any global information such as the eigenvalue of the Laplacian matrix related to the communication topologies, the upper boundness of the leader's input, and so on. The algorithms to determine parameters of control protocols are also presented. Furthermore, the closed-loop stability of GLMASs is proven by the Lyapunov theory. Finally, numerical simulations are given to verify the effectiveness of theoretical results.