Mean Field Control by Stochastic Koopman Operator via a Spectral Method

TL;DR

This paper introduces a data-driven spectral method using stochastic Koopman operators to linearize and solve mean field control problems, enabling efficient and robust large-scale population management.

Contribution

It develops a novel spectral approach leveraging Koopman operator theory to linearize mean field control problems in a data-driven manner.

Findings

Derives a linear model for mean field control via Koopman decomposition.

Develops a model predictive control framework for robustness and efficiency.

Enhances applicability of mean field control in complex systems.

Abstract

Mean field control provides a robust framework for coordinating large-scale populations with complex interactions and has wide applications across diverse fields. However, the inherent nonlinearity and the presence of unknown system dynamics pose significant challenges for developing effective analytic or numerical solutions. There is a pressing need for data-driven methodologies to construct accurate models and facilitate efficient planning and control. To this end, we leverage Koopman operator theory to advance solution methods for mean field control problems. Our approach involves exploring stochastic Koopman operators using spectral analysis techniques. Through Koopman decomposition, we derive a linear model for mean field control problems in a data-driven fashion. Finally, we develop a model predictive control framework to achieve robust control and reduce the computational complexity for mean field control problems, thereby enhancing the efficacy and applicability of mean field control solutions in various domains.