Optimal control laws for the model of information diffusion in a social group |
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Authors: | Email author" target="_blank">S?N?AvvakumovEmail author Yu?N?Kiselev |
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Institution: | 1.Faculty of Computational Mathematics and Cybernetics,Moscow State University,Moscow,Russia |
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Abstract: | The article investigates two models of information diffusion in a social group. The dynamics of the process is described by
a one-dimensional controlled Riccati differential equation. Our two models differ from the original model of K. V. Izmodenova
and A. P. Mikhailov in the choice of the functional being optimized. Two different choices of the optimand functional are
considered. The optimal control problems are solved by the Pontryagin maximum principle. It is shown that the optimal control
program is a relay function of time with at most one switching point. Conditions on the problem parameters are proposed that
are easy to check and guarantee the existence of an optimal-control switching point. The theoretical analysis leads to a one-dimensional
convex minimization problem to find the optimal-control switching point. The article also describes an alternative approach
to the construction of the optimal solution, which does not resort to the maximum principle and instead utilizes a special
representation of the optimand functional and works with reachability sets that are independent of the functional. For the
two models considered in this article optimal feedback controls are derived from the programmed optimal controls. |
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