On an optimal control strategy in a kinetic social dynamics model

Damián A. Knopoff 1 , 2  and Germán A. Torres 3 , 4
  • 1 Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba,, Córdoba, Argentina
  • 2 Centro de Investigación y Estudios de Matemática, CONICET, Godoy Cruz 2290,, Buenos Aires, Argentina
  • 3 Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste,, Corrientes, Argentina
  • 4 Instituto de Modelado e Innovacion Tecnologica, CONICET, Godoy Cruz 2290,, Buenos Aires, Argentina


Kinetic models have so far been used to model wealth distribution in a society. In particular, within the framework of the kinetic theory for active particles, some important models have been developed and proposed. They involve nonlinear interactions among individuals that are modeled according to game theoretical tools by introducing parameters governing the temporal dynamics of the system. In this present paper we propose an approach based on optimal control tools that aims to optimize this evolving dynamics from a social point of view. Namely, we look for time dependent control variables concerning the distribution of wealth that can be managed, for instance, by the government, in order to obtain a given social profile.

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