Model Predictive Mean Field Games for Controlling Multi-Agent Systems
This work addresses scalability and robustness issues in multi-agent systems, offering an incremental improvement over existing mean field game methods.
The paper tackles the trade-off between performance and scalability in multi-agent control by proposing a model predictive mean field game (MP-MFG) that estimates agent density and generates inputs via model predictive control, achieving higher robustness than conventional MFGs, with numerical results showing it outperforms MFGs when agent models have errors or agent numbers are small.
When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics describing the density profile of agents from their microscopic dynamics. To effectively use the MFG, we propose a model predictive MFG (MP-MFG), which estimates the agent population density profile with using kernel density estimation and manages the input generation with model predictive control. The proposed MP-MFG generates control inputs by monitoring the agent population at each time step, and thus achieves higher robustness than the conventional MFG. Numerical results show that the MP-MFG outperforms the MFG when the agent model has modeling errors or the number of agents in the system is small.