Target formation on the circle by monotone system design

TL;DR

This paper extends positivity and Perron-Frobenius theory to nonlinear consensus algorithms on the circle, providing tools for designing protocols that ensure monotonic convergence to desired formations.

Contribution

It introduces a novel framework for analyzing and designing nonlinear consensus algorithms on the circle using generalized positivity concepts.

Findings

Established convergence criteria for nonlinear circle consensus algorithms.

Developed design tools for monotone convergence to target formations.

Extended Perron-Frobenius theory to nonlinear circular systems.

Abstract

Positivity and Perron-Frobenius theory provide an elegant framework for the convergence analysis of linear consensus algorithms. Here we consider a generalization of these ideas to the analysis of nonlinear consensus algorithms on the circle and establish tools for the design of consensus protocols that monotonically converge to target formations on the circle.