Optimal Leader–Follower Control for the Fractional Opinion Formation Model

被引：0
作者：
Ricardo Almeida
Agnieszka B. Malinowska
Tatiana Odzijewicz
机构：
[1] University of Aveiro,Center for Research and Development in Mathematics ad Applications (CIDMA), Department of Mathematics
[2] Bialystok University of Technology,Faculty of Computer Science
[3] Warsaw School of Economics,Department of Mathematics and Mathematical Economics
来源：
Journal of Optimization Theory and Applications | 2019年 / 182卷
关键词：
Opinion formation models; Consensus problem; Fractional derivatives; Optimal control; Variational integrators; 49K99; 49M25; 26A33; 39A99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper deals with an opinion formation model, that obeys a nonlinear system of fractional-order differential equations. We introduce a virtual leader in order to attain a consensus. Sufficient conditions are established to ensure that the opinions of all agents globally asymptotically approach the opinion of the leader. We also address the problem of designing optimal control strategies for the leader so that the followers tend to consensus in the most efficient way. A variational integrator scheme is applied to solve the leader–follower optimal control problem. Finally, in order to verify the theoretical analysis, several particular examples are presented.
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页码：1171 / 1185
页数：14
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