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arXiv · 2312.06422

Mean field limits for discrete-time dynamical systems via kernel mean embeddings

Christian Fiedler·Michael Herty·Sebastian Trimpe
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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.

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Christian Fiedler, Michael Herty, Sebastian Trimpe. 2023-12-11. Mean field limits for discrete-time dynamical systems via kernel mean embeddings. https://arxiv.org/abs/2312.06422

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