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

arXiv (Cornell University)

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.

Authors 3

1. Christian Fiedler Aachen Data Science in Mechanical Engineering (DSME) Institute for Geometry and Practical Mathe- matics (IGPM)

   RWTH Aachen University

   Affiliation as printed

   Data Science in Mechanical Engineering (DSME) , RWTH Aachen University , Aachen , Germany

   Institute for Geometry and Practical Mathe- matics (IGPM) , RWTH Aachen University , Aachen Germany

2. Michaël Herty Aachen Data Science in Mechanical Engineering (DSME)

   RWTH Aachen University

   Affiliation as printed

   Data Science in Mechanical Engineering (DSME) , RWTH Aachen University , Aachen , Germany

3. Sebastian Trimpe Aachen Data Science in Mechanical Engineering (DSME)

   RWTH Aachen University

   Affiliation as printed

   Data Science in Mechanical Engineering (DSME) , RWTH Aachen University , Aachen , Germany