The projection method for continuous-time consensus seeking

TL;DR

This paper introduces a projection method to achieve consensus in continuous-time multi-agent systems, especially when the dependency graph lacks a spanning in-tree, extending discrete-time techniques to continuous dynamics.

Contribution

It characterizes the convergence region for continuous-time consensus and adapts the orthogonal projection method from discrete to continuous-time settings.

Findings

Consensus can be achieved without a spanning in-tree using the projection method.

The convergence region for the continuous-time consensus algorithm is explicitly characterized.

The projection method extends discrete-time coordination techniques to continuous-time systems.

Abstract

For the case where the dependency digraph has no spanning in-tree, we characterize the region of convergence of the basic continuous-time distributed consensus algorithm and show that consensus can be achieved by employing the method of orthogonal projection, which has been proposed for the discrete-time coordination problem.