Time‐varying group formation analysis and design for general linear multi‐agent systems with directed topologies

Summary Time‐varying group formation control problems for general linear multi‐agent systems with directed topologies are studied. Different from the traditional complete formation, where only one formation is realized by the multi‐agent system, in the group formation, there could be multiple time‐varying sub‐formations. Firstly, a time‐varying group formation protocol is constructed by local neighboring relative information. Then nonsingular transformations are applied to the closed‐loop multi‐agent systems. Sufficient conditions for the multi‐agent systems to achieve time‐varying group formation are further presented together with the time‐varying group formation feasibility constraints. Explicit expressions of the subgroup formation reference functions are derived to describe the macroscopic movement of the time‐varying subgroup formations. Moreover, an approach to design the time‐varying group formation protocol is proposed by solving an algebraic Riccati equation. Finally, a numerical example with three subgroups is provided to demonstrate the effectiveness of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.