Consensus and Synchronization of Multi-agent Systems over Finite Fields -- Graph Topologies

TL;DR

This paper develops algorithms for designing communication topologies in multi-agent systems with finite state-spaces, ensuring consensus and synchronization while addressing NP-hardness issues.

Contribution

It introduces two new algorithms for efficiently generating admissible communication topologies in finite-state multi-agent systems.

Findings

Algorithms successfully generate admissible topologies.

Simulations confirm the effectiveness of the proposed methods.

Finite-state agents exhibit resilience to communication noise.

Abstract

This paper brings cooperative protocols for multi-agent systems with agents having a finite state-space. Both scalar single-integrator consensus and general LTI systems synchronization are considered. Systems having a finite state-space describe agents with minimal memory capacity processing only a finite alphabet. Such systems are remarkably resilient to communication noise. The crucial problem, however, is to construct the admissible communication topology, which is NP-hard. We address this by efficiently exploring the subsets of admissible matrices and propose two new algorithms to generate the topologies. Simulations validate the proposed approach.