Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies

Abstract

This article studies a consensus problem for a group of high-order dynamic agents with fixed and switching topologies. Two linear consensus protocols, which only depend on the agent's own information and its neighbours' partial information, are proposed, respectively, for the group with and without communication time-delays. For the case of fixed topology and zero communication time-delay, a necessary and sufficient condition for the consensus is established. The parameter design of the protocol is also discussed. Under switching topology, the consensus is investigated for two cases: the case of zero communication time-delay and the case of nonuniform communication time-delays. For each case, a sufficient condition for the consensus is provided. Moreover, for a group of double/triple-integrator agents with fixed topology and uniform constant time-delay, some necessary and sufficient conditions for the consensus are given. Finally, numerical simulations are worked out to illustrate the effectiveness of the theoretical results.

Keywords:

• distributed control
• consensus problems
• high-order dynamic agents
• multi-agent systems
• switching topology
• time-delays

Acknowledgements

This work was supported by NSFC (60674050, 60736022 and 60528007) and 11-5 project (A2120061303). The authors are very grateful to reviewers and editor for their valuable comments to improve the presentation of the article.