Scalable second-order consensus of hierarchical groups
CoRR(2024)
Abstract
Motivated by widespread dominance hierarchy, growth of group sizes, and
feedback mechanisms in social species, we are devoted to exploring the scalable
second-order consensus of hierarchical groups. More specifically, a
hierarchical group consists of a collection of agents with double-integrator
dynamics on a directed acyclic graph with additional reverse edges, which
characterize feedback mechanisms across hierarchical layers. As the group size
grows and the reverse edges appear, we investigate whether the absolute
velocity protocol and the relative velocity protocol can preserve the system
consensus property without tuning the control gains. It is rigorously proved
that the absolute velocity protocol is able to achieve completely scalable
second-order consensus but the relative velocity protocol cannot. This result
theoretically reveals how the scalable coordination behavior in hierarchical
groups is determined by local interaction rules. Moreover, we develop a
hierarchical structure in order to achieve scalable second-order consensus for
networks of any size and with any number of reverse edges.
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