# A parabolic approach to the control of opinion spreading

## TL;DR

This paper presents a novel control strategy for nonlinear opinion spreading models, providing explicit cost estimates and leveraging techniques from parabolic PDE controllability to achieve consensus.

## Contribution

It introduces a parabolic PDE-based approach to control opinion dynamics, with explicit cost bounds depending on agent number and control horizon.

## Key findings

- Explicit exponential cost estimates derived
- Control strategy applicable to large agent populations
- Link between opinion models and semilinear parabolic equations

## Abstract

We analyze the problem of controlling to consensus a nonlinear system modeling opinion spreading. We derive explicit exponential estimates on the cost of approximately controlling these systems to consensus, as a function of the number of agents N and the control time-horizon T. Our strategy makes use of known results on the controllability of spatially discretized semilinear parabolic equations. Both systems can be linked through time-rescaling