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RWTH Publication No: 975105 2023 
TITLE 
Mean field limits for discretetime dynamical systems via kernel mean embeddings 
AUTHORS 
Christian Fiedler, Michael Herty, Sebastian Trimpe 
ABSTRACT 
Mean field limits are an important tool in the
context of largescale dynamical systems, in particular, when
studying multiagent and interacting particle systems. While
the continuoustime theory is welldeveloped, few works have
considered mean field limits for deterministic discretetime
systems, which are relevant for the analysis and control of
largescale discretetime multiagent system. We prove existence
results for the mean field limit of very general discretetime
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
discretetime dynamical systems. 
KEYWORDS 

DOI 
10.1109/LCSYS.2023.3341280 