Steering Opinion Dynamics in Signed Time-Varying Networks via External Control Input

TL;DR

This paper develops a control strategy for steering opinions in complex multi-agent networks with signed, time-varying interactions, ensuring convergence to desired opinion states despite natural clustering tendencies.

Contribution

It introduces a novel controller design method for influencing opinion dynamics in signed, time-varying networks, overcoming natural polarization effects.

Findings

Exponential convergence of opinions to desired states.

Effective control design for complex dynamic networks.

Validation through extensive numerical simulations.

Abstract

This paper studies targeted opinion formation in multi-agent systems evolving over signed, time-varying directed graphs. The dynamics of each agent's state follow a Laplacian-based update rule driven by both cooperative and antagonistic interactions in the presence of exogenous factors. We formulate these exogenous factors as external control inputs and establish a suitable controller design methodology enabling collective opinion to converge to any desired steady-state configuration, superseding the natural emergent clustering or polarization behavior imposed by persistently structurally balanced influential root nodes. Our approach leverages upper Dini derivative analysis and Gr\"onwall-type inequalities to establish exponential convergence for opinion magnitude towards the desired steady state configuration on networks with uniform quasi-strong $\delta$-connectivity. Finally, the theoretical results are validated through extensive numerical simulations.