# Performance bounds for the mean-field limit of constrained dynamics

arXiv: https://arxiv.org/abs/1511.08364 · HTML: https://mlsanity.com/paper/1511.08364/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2015.

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

- [Reproducing kernel Hilbert spaces in the mean field limit](https://mlsanity.com/paper/2302.14446/) (2023)
- [On kernel-based statistical learning in the mean field limit](https://mlsanity.com/paper/2310.18074/) (2023)

## Abstract (arXiv)

In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually hard to compute) optimal control and the MPC approach is investigated theoretically in the mean-field limit. We establish a computable and provable bound on the difference in the cost functional for MPC controlled and optimal controlled system dynamics in the mean-field limit. The result of the present work extends previous findings for systems of ordinary differential equations. Numerical results in the mean-field setting are given.