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Optimal leader-following consensus of fractional opinion formation models
Journal of Computational and Applied Mathematics ( IF 2.4 ) Pub Date : 2020-06-01 , DOI: 10.1016/j.cam.2020.112996
Ricardo Almeida , Rafał Kamocki , Agnieszka B. Malinowska , Tatiana Odzijewicz

This paper deals with a control strategy enforcing consensus in a fractional opinion formation model with leadership, where the interaction rates between followers and the influence rate of the leader are functions of deviations of opinions between agents. The fractional-order derivative determines the impact of the memory during the opinion evolution. The problem of leader-following consensus control is cast in the framework of nonlinear optimal control theory. We study a finite horizon optimal control problem, in which deviations of opinions between agents and with respect to the leader are penalized along with the control that is applied only to the leader. The existence conditions for optimal consensus control are proved and necessary optimality conditions for the considered problem are derived. The results of the paper are illustrated by some examples.



中文翻译:

分数意见形成模型的最优跟随者共识

本文提出了一种在领导带分数意见形成模型中实施共识的控制策略,其中追随者之间的互动率和领导者的影响率是主体之间意见偏差的函数。分数阶导数确定了意见演变过程中记忆的影响。前导跟随共识控制问题是在非线性最优控制理论的框架内提出的。我们研究了一个有限水平的最优控制问题,其中,代理之间以及相对于领导者的观点偏差与仅应用于领导者的控制一起受到了惩罚。证明了最优共识控制的存在条件,并得出了所考虑问题的必要最优条件。

更新日期:2020-06-01
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