Control of collective dynamics with time-varying weights

TL;DR

This paper investigates controlling opinion dynamics where influence weights change over time, proposing strategies to steer all agents to consensus, analyzing controllability, and illustrating results with numerical simulations.

Contribution

It introduces a control framework for opinion models with time-varying influence weights, including controllability analysis and control design methods.

Findings

Controllability is established for systems with and without mass constraints.

Steepest descent methods effectively design control strategies.

Numerical simulations demonstrate successful consensus control.

Abstract

This paper focuses on a model for opinion dynamics, where the influence weights of agents evolve in time. We formulate a control problem of consensus type, in which the objective is to drive all agents to a final target point under suitable control constraints. Controllability is discussed for the corresponding problem with and without constraints on the total mass of the system, and control strategies are designed with the steepest descent approach. The mean-field limit is described both for the opinion dynamics and the control problem. Numerical simulations illustrate the control strategies for the finite-dimensional system.