The role of local bounds on neighborhoods in the network for scale-free state synchronization of multi-agent systems

TL;DR

This paper establishes conditions for achieving scale-free state synchronization in multi-agent systems, highlighting the crucial role of local neighborhood bounds in protocol design for both continuous and discrete-time systems.

Contribution

It provides necessary and sufficient conditions for scale-free synchronization and analyzes the impact of local neighborhood bounds on protocol effectiveness.

Findings

Local bounds are key to synchronization success.

Conditions are derived for both continuous and discrete-time systems.

Protocol design can be optimized using local neighborhood information.

Abstract

This paper provides necessary and sufficient conditions for the existence of solutions to the state synchronization problem of homogeneous multi-agent systems (MAS) via scale-free linear dynamic non-collaborative protocol for both continuous- and discrete-time. These conditions guarantee for which class of MAS, one can achieve scale-free state synchronization. We investigate protocol design with and without utilizing local bounds on neighborhood. The results show that the availability of local bounds on neighborhoods plays a key role.