Pinning consensus in networks of multiagents via a single impulsive controller

TL;DR

This paper studies how a single impulsive controller can achieve consensus in multiagent networks by providing conditions on impulsive strength and timing, especially when the network has a spanning tree.

Contribution

It introduces a sufficient condition for pinning consensus using only one impulsive controller on the root node, depending on graph eigenvectors and impulsive parameters.

Findings

Consensus can be achieved with a single impulsive controller on the root node.

The permissible impulsive strength range depends on the graph's eigenvector.

Impulses can be sparse with lower bounded intervals.

Abstract

In this paper, we discuss pinning consensus in networks of multiagents via impulsive controllers. In particular, we consider the case of using only one impulsive controller. We provide a sufficient condition to pin the network to a prescribed value. It is rigorously proven that in case the underlying graph of the network has spanning trees, the network can reach consensus on the prescribed value when the impulsive controller is imposed on the root with appropriate impulsive strength and impulse intervals. Interestingly, we find that the permissible range of the impulsive strength completely depends on the left eigenvector of the graph Laplacian corresponding to the zero eigenvalue and the pinning node we choose. The impulses can be very sparse, with the impulsive intervals being lower bounded. Examples with numerical simulations are also provided to illustrate the theoretical results.