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Bipartite Consensus of Discrete-Time Double-Integrator Multi-Agent Systems with Measurement Noise

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Abstract

The effects of measurement noise are investigated in the context of bipartite consensus of multi-agent systems. In the system setting, discrete-time double-integrator dynamics are assumed for the agent, and measurement noise is present for the agent receiving the state information from its neighbors. Time-varying stochastic bipartite consensus protocols are designed in order to lessen the harmful effects of the noise. Consequently, the state transition matrix of the closed-loop system is analyzed, and sufficient and necessary conditions for the proposed protocol to be a mean square bipartite consensus protocol are given with the help of linear transformation and algebraic graph theory. It is proven that the signed digraph to be structurally balanced and having a spanning tree are the weakest communication assumptions for ensuring bipartite consensus. In particular, the proposed protocol is a mean square bipartite average consensus one if the signed digraph is also weight balanced.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Cuiqin Ma

  2. No. 1 Senior Middle School of Qufu, Qufu, 273165, China

    Weiwei Zhao

  3. College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, China

    Yunbo Zhao

Authors
  1. Cuiqin Ma
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  2. Weiwei Zhao
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  3. Yunbo Zhao
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Corresponding author

Correspondence to Cuiqin Ma.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61104136, 61673350, 61573228, the Natural Science Foundation of Shandong Province under Grant Nos. ZR2010FQ002, ZR2016FQ09, Postgraduate Education Innovation Program of Shandong Province under Grant No. SDYY16088, and the Young Teacher Capability Enhancement Program for Overseas Study, Qufu Normal University.

This paper was recommended for publication by Editor SUN Jian.

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Ma, C., Zhao, W. & Zhao, Y. Bipartite Consensus of Discrete-Time Double-Integrator Multi-Agent Systems with Measurement Noise. J Syst Sci Complex 31, 1525–1540 (2018). https://doi.org/10.1007/s11424-018-7363-x

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  • DOI: https://doi.org/10.1007/s11424-018-7363-x

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