# Kinetic description of optimal control problems and applications to opinion consensus

arXiv: https://arxiv.org/abs/1401.7798 · HTML: https://mlsanity.com/paper/1401.7798/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2014.

## Built on by (most cited first, 2 of 2)

- [A kinetic approach to consensus-based segmentation of biomedical images](https://mlsanity.com/paper/2211.05226/) (2022)
- [A Multiscale Kinetic Framework for Image Segmentation: From Particle Systems to Continuum Models](https://mlsanity.com/paper/2605.28619/) (2026)

## Abstract (arXiv)

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.