Distributed impulsive group consensus in second-order multi-agent systems under directed topology

Abstract

This paper investigates the impulsive group consensus problems of second-order multi-agent systems under directed network topology with acyclic partition. Two distributed impulsive sampled-data protocols are presented to realise group consensus for both cases with leaders and leaderless, and then some simple yet generic criteria on convergence for such algorithms are established. It is shown that, for the case with leaderless, a feature of the present protocols is to give an explicit expression of group consensus states in terms of the initial values of the agents, which allows us to develop a simple approach yielding the desired group or cluster consensus. While for the case of virtual leaders, a pinning-like tracking technique is effectively designed to regulate all the agents access to the virtual leaders respectively for the purpose of practical control strategy. Finally, simulation results are presented to illustrate the effectiveness of the theoretical analysis.

Keywords:

• group consensus
• cluster consensus
• impulsive control
• acyclic partition
• multi-agent systems

Acknowledgements

The authors wishes to thank the editor and the reviewers for their insightful and constructive comments, which improved this paper significantly.

Additional information

Funding

This work is supported by the National Science Foundation of China [grant number 10972129], [grant number 10832006], [grant number 11272191]; Specialized Research Foundation for the Doctoral Program of Higher Education [grant number 200802800015]; the Shanghai Leading Academic Discipline Project, [Project no. S 30106].