Coordination on Time-Varying Antagonistic Networks

Abstract

This paper studies coordination problem for time-varying networks suffering from antagonistic information, quantified by scaling parameters. By such a manner, interacting property of the participating individuals and antagonistic information can be quantified in a fully decoupled perspective, thus benefiting from merely directed spanning tree hypothesis is needed, in the sense of usual algebraic graph theory. We start with rigorous argument on the existence of weighted gain, and then derive relation among weighted gain, scaling parameter and Laplacian matrix guaranteeing antagonistic information cannot diverge system state. Based on these arguments, we devise coordination algorithm constrained by topology-dependent average time condition, thus relaxing the examination of directed spanning tree requirement for the union graph that is usually intractable. Moreover, the induced theoretical results are applied to time-varying networks with several mutually uninfluenced agents, in accompanying with some discussions and comparisons with respect to the existing developments.

Consensus for cooperative–competitive network systems: An impulsive perspective

“…That is to say, sgn(𝜌 j ) ≠ sgn(𝛼 j ) while guaranteeing this property in matrix D can merely be applicable for nodes related to Ĝ. It is worthy to highlight that this a problem has not been discussed by 39 in which  = I n and D = I n are used.…”