Hybrid coordination of multi-agent networks with hierarchical leaders

• A hierarchical multi-agent network with major and minor leader is established.
• Hybrid coordination means minors achieve formation and followers obtain consensus.
• For static major leader with follower groups, hybrid coordination relies on topology.
• For coupling groups, proper control parameters and adjacency matrix are designed.
• Dynamic hybrid coordination is reached for moving major leader with hierarchy delays.

In this paper, the hybrid coordination problem of multi-agent networks with hierarchical leaders is investigated. Firstly, for the case of static major leader with uncoupled follower groups, a necessary and sufficient condition is given for all minor leaders to attain the expected formation and follower groups asymptotically converge to their given desired states. Secondly, for the case of static major leader with coupling follower groups, a sufficient condition on control parameters and the weighted adjacency matrix for the hybrid coordination is provided. Thirdly, for the case of moving major leader with hierarchy delays, a necessary and sufficient condition for the multi-agent network to derive desired performance is also obtained. Finally, some numerical examples are presented to illustrate the theoretical results.