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Optimal Leader–Follower Control for the Fractional Opinion Formation Model

Author

Listed:
  • Ricardo Almeida

    (University of Aveiro)

  • Agnieszka B. Malinowska

    (Bialystok University of Technology)

  • Tatiana Odzijewicz

    (Warsaw School of Economics)

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.

Suggested Citation

  • Ricardo Almeida & Agnieszka B. Malinowska & Tatiana Odzijewicz, 2019. "Optimal Leader–Follower Control for the Fractional Opinion Formation Model," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1171-1185, September.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-018-1363-9
    DOI: 10.1007/s10957-018-1363-9
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    References listed on IDEAS

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    1. Katarzyna Sznajd-Weron & Józef Sznajd, 2000. "Opinion Evolution In Closed Community," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1157-1165.
    2. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
    3. Mohammad Afshar & Masoud Asadpour, 2010. "Opinion Formation by Informed Agents," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 13(4), pages 1-5.
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