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arXiv · 1401.7798

Kinetic description of optimal control problems and applications to opinion consensus

Giacomo Albi·Michael Herty·Lorenzo Pareschi
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Abstract

In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under constraints. For this problem a Boltzmann-type equation based on a model predictive control formulation is introduced and discussed. In particular, the receding horizon strategy permits to embed the minimization of suitable cost functional into binary particle interactions. The corresponding Fokker-Planck asymptotic limit is also derived and explicit expressions of stationary solutions are given. Several numerical results showing the robustness of the present approach are finally reported.

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Giacomo Albi, Michael Herty, Lorenzo Pareschi. 2014-01-30. Kinetic description of optimal control problems and applications to opinion consensus. https://arxiv.org/abs/1401.7798

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