Optimal Leader–Follower Control for the Fractional Opinion Formation Model

Ricardo Almeida (), Agnieszka B. Malinowska () and Tatiana Odzijewicz ()
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Ricardo Almeida: University of Aveiro
Agnieszka B. Malinowska: Bialystok University of Technology
Tatiana Odzijewicz: Warsaw School of Economics

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 3, No 16, 1185 pages

Abstract: Abstract 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.

Keywords: Opinion formation models; Consensus problem; Fractional derivatives; Optimal control; Variational integrators; 49K99; 49M25; 26A33; 39A99 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1363-9

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