Large-Scale Multiagent System Tracking Control Using Mean Field Games

Area of Science:

• Control Theory
• Artificial Intelligence
• Multiagent Systems

Background:

• Traditional control methods struggle with the "Curse of Dimensionality" in large-scale multiagent systems (MASs).
• A new intelligent design is required to manage systems with a vast number of agents.
• Existing approaches often require high-dimensional data from individual agents, posing scalability challenges.

Purpose of the Study:

• To develop an advanced intelligent tracking control method for large-scale MASs.
• To address the computational complexity and scalability issues inherent in large MASs.
• To integrate Mean Field Game (MFG) theory with reinforcement learning for enhanced control.

Main Methods:

• Employed Mean Field Game (MFG) theory integrated with reinforcement learning.
• Utilized approximate dynamic programming to create a novel MFG-based algorithm.
• Implemented three neural networks (NNs) per agent for approximating mean field control solutions.
• Analyzed NN performance using Lyapunov stability methods.

Main Results:

• The proposed MFG-based control calculates optimal strategies using a unified, fixed-dimension probability density function (pdf).
• This approach avoids processing high-dimensional information from numerous individual agents.
• Simulations demonstrated the algorithm's effectiveness in both linear and nonlinear tracking control scenarios.

Conclusions:

• The integration of MFG theory and reinforcement learning offers an effective solution for tracking control in large-scale MASs.
• The developed algorithm successfully mitigates the curse of dimensionality.
• The use of neural networks and Lyapunov analysis ensures robust performance and stability.