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Zbl 1226.93008
Chen, Gang; Lewis, Frank L.; Xie, Lihua
Finite-time distributed consensus via binary control protocols. (English)
[J] Automatica 47, No. 9, 1962-1968 (2011). ISSN 0005-1098

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 2000:: *93A14 Decentralized systems
94C15 Appl. of graph theory to circuits and networks
93C15 Control systems governed by ODE
93C10 Nonlinear control systems

Keywords: cooperative control; network consensus; pinning control; multi-agent systems

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