Kinetic description of optimal control problems and applications to opinion consensus
Optimization and Control
2014-01-31 v1 Adaptation and Self-Organizing Systems
Physics and Society
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.
Cite
@article{arxiv.1401.7798,
title = {Kinetic description of optimal control problems and applications to opinion consensus},
author = {Giacomo Albi and Michael Herty and Lorenzo Pareschi},
journal= {arXiv preprint arXiv:1401.7798},
year = {2014}
}
Comments
25 pages, 18 figures