Non-invasive control of the fractional Hegselmann-Krause type model

TL;DR

This paper develops a fractional order Hegselmann-Krause model with leadership, proposing an optimal control strategy to achieve consensus, validated through numerical examples using a fractional Pontryagin Maximum Principle.

Contribution

It introduces a novel fractional control approach for the Hegselmann-Krause model with leadership, deriving necessary optimality conditions and demonstrating effectiveness.

Findings

Control strategy successfully guides system to consensus

Numerical examples confirm the effectiveness of the control method

Fractional Pontryagin Maximum Principle is applicable to this model

Abstract

In this paper, the fractional order Hegselmann-Krause type model with leadership is studied.We seek an optimal control strategy for the system to reach a consensus in such a way that the control mechanism is included in the leader dynamics. Necessary optimality conditions are obtained by the use of a fractional counterpart of Pontryagin Maximum Principle. The effectiveness of the proposed control strategy is illustrated by numerical examples.