Mean-Field Limits for Discrete-Time Dynamical Systems via Kernel Mean Embeddings

IEEE Control Systems Letters, vol. 7, pp. 3914–3919

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 Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

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

2. Michaël Herty Aachen Institute for Geometry and Practical Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Geometry and Practical Mathematics, RWTH Aachen University, Aachen, Germany

   Institute for Geometry and Practical Mathematics (IGPM), RWTH Aachen University, Aachen, Germany

3. Sebastian Trimpe Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

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