Finite-Time Time-Varying Group Formation Tracking for High-Order Multi-Agent Systems with Mismatched Disturbances under Directed Graphs

Finite-time time-varying group formation (FT-TVGF) tracking control problems for high-order multi-agent systems (MASs) are studied in this paper. Different from previous work, the approaches proposed in this paper combine group formation tracking control with finite-time control, not only that, the agents in each group can achieve time-varying sub-formations and the relative configuration between different groups can be adjusted simultaneously. First, all agents are divided into three types, including the virtual leader, the group leader, and the follower. The virtual leader is added to plan the trajectory of MASs. Subgroups can be interacted with each other by the communication among group leaders. Followers achieve the finite-time formation tracking of group leaders. Then the disturbance observer is constructed to estimate the mismatched disturbances of all group leaders and followers in finite time. Furthermore, based on finite time control theory and observer theory, a distributed control protocol is presented to make MASs realize FT-TVGF tracking under directed graph. The proof of close-loop stability of MASs is accomplished using Lyapunov theory. Finally, numerical simulations verify the theoretical analysis of this paper.