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**Finite-time formation control for multi-agent systems.**
*(English)*
Zbl 1180.93006

Summary: We develop a new finite-time formation control framework for multi-agent systems with a large population of members. In this framework, we divide the formation information into two independent parts, namely, the global information and the local information. The global formation information decides the geometric pattern of the desired formation. Furthermore, it is assumed that only a small number of agents, which are responsible for the navigation of the whole team, can obtain the global formation information, and the other agents regulate their positions by the local information in a distributed manner. This approach can greatly reduce the data exchange and can easily realize various kinds of complex formations. As a theoretical preparation, we first propose a class of nonlinear consensus protocols, which ensures that the related states of all agents will reach an agreement in a finite time under suitable conditions. And then we apply these consensus protocols to the formation control, including time-invariant formation, time-varying formation and trajectory tracking, respectively. It is shown that all agents will maintain the expected formation in a finite time. Finally, several simulations are worked out to illustrate the effectiveness of our theoretical results.

### MSC:

93A14 | Decentralized systems |

93B50 | Synthesis problems |

94C15 | Applications of graph theory to circuits and networks |

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\textit{F. Xiao} et al., Automatica 45, No. 11, 2605--2611 (2009; Zbl 1180.93006)

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