Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs

Abstract

In this paper, finite-time multi-agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative. A nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time. If the signed graph is structurally balanced, then the final consensus states of all agents are the same in modulus but not in sign. Otherwise, if the signed graph is structurally unbalanced, then the states of all agents converge to zero. Moreover, the final consensus states of agents can be provided uniformly regarding a signed-average quantity that depends on both the initial states of agents and the topology structure of the whole multi-agent network. Numerical simulations illustrate that the protocol is effective in achieving the finite-time consensus of agents under signed graphs and can particularly solve the finite-time average consensus problem of agents when their associated graph has all positive edge weights.

Keywords:

• finite-time consensus
• multi-agent networks
• signed graphs
• structural balance
• structural unbalance
• average consensus

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments and suggestions which improved the quality and presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper was supported by the National Basic Research Program of China (973 Program) [grant number 2012CB821200], [grant number 2012CB821201]; the National Natural Science Foundation of China (NSFC) [grant number 61473010], [grant number 61134005], [grant number 61221061], [grant number 61327807], [grant number 61320106006]; the Fundamental Research Funds for the Central Universities.