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**Finite-time distributed consensus via binary control protocols.**
*(English)*
Zbl 1226.93008

Summary: This paper investigates the finite-time distributed consensus problem for multi-agent systems using a binary consensus protocol and the pinning control scheme. Compared with other consensus algorithms which need the complete state or output information of neighbors, the proposed algorithm only requires sign information of the relative state measurements, that is, the differences between a node’s state and that of its neighbors. This corresponds to only requiring a single-bit quantization error relative to each neighbor. This signum protocol is realistic in terms of observed behavior in animal groups, where relative motion is determined not by full time-signal measurements, but by coarse estimates of relative heading differences between neighbors. The signum protocol does not require explicit measurement of time signals from neighbors, and hence has the potential to significantly reduce the requirements for both computation and sensing. Analysis of discontinuous dynamical systems is used, including the Filippov solutions and set-valued Lie derivative. Based on the second-order information on the evolution of Lyapunov functions, the conditions that guarantee the finite-time consensus for the systems are identified. Numerical examples are given to illustrate the theoretical results.

### MSC:

93A14 | Decentralized systems |

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

93C15 | Control/observation systems governed by ordinary differential equations |

93C10 | Nonlinear systems in control theory |

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\textit{G. Chen} et al., Automatica 47, No. 9, 1962--1968 (2011; Zbl 1226.93008)

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