Mean field limits for discrete-time dynamical systems via kernel mean embeddings
Abstract
Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered mean field limits for deterministic discrete-time systems, which are relevant for the analysis and control of large-scale discrete-time multiagent system. We prove existence results for the mean field limit of very general discrete-time control systems, for which we utilize kernel mean embeddings. These results are then applied in a typical optimal control setup, where we establish the mean field limit of the relaxed dynamic programming principle. Our results can serve as a rigorous foundation for many applications of mean field approaches for discrete-time dynamical systems.
Cite
@article{arxiv.2312.06422,
title = {Mean field limits for discrete-time dynamical systems via kernel mean embeddings},
author = {Christian Fiedler and Michael Herty and Sebastian Trimpe},
journal= {arXiv preprint arXiv:2312.06422},
year = {2023}
}
Comments
Accepted at IEEE Control Systems Letters