Persistence based analysis of consensus protocols for dynamic graph networks

TL;DR

This paper introduces a novel persistence-based analysis method for consensus protocols in dynamic graph networks with time-varying and singular edge weights, enabling precise convergence rate computation.

Contribution

It develops a new analysis technique using classical persistence of excitation concepts to study convergence in multi-agent systems with smoothly varying, singular, time-dependent edge weights.

Findings

Allows analysis of convergence with smooth edge weight variations

Enables precise computation of convergence rates

Extends existing results to more general dynamic networks

Abstract

This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These results are based on the analysis of a system switching between piecewise constant and time-invariant dynamics. This work introduces a new analysis technique relying upon classical notions of persistence of excitation to study the convergence properties of the time-varying multi-agent dynamics. Since the individual edge weights pass through singularities and vary with time, the closed-loop dynamics consists of a non-autonomous linear system. Instead of simplifying to a piecewise continuous switched system as in literature, smooth variations in edge weights are allowed, albeit assuming an underlying persistence condition which characterizes sufficient inter-agent communication to reach consensus. The consensus task is converted to edge-agreement in order to study a stabilization problem to which classical persistence based results apply. The new technique allows precise computation of the rate of convergence to the consensus value.