A Novel Mean-Field-Game-Type Optimal Control for Very Large-Scale Multiagent Systems

Area of Science:

• Control Theory
• Artificial Intelligence
• Game Theory

Background:

• Large-scale multiagent systems (MASs) present significant computational challenges due to high dimensionality.
• Existing control methods struggle with uncertain dynamics and massive agent populations.
• Mean-field game (MFG) theory offers a framework for analyzing large MASs by approximating individual agent behavior based on population averages.

Purpose of the Study:

• To develop a decentralized adaptive optimal controller for large-scale MASs with uncertain dynamics.
• To address the "curse of dimensionality" and reduce computational complexity in MAS control.
• To integrate MFG theory with self-organizing neural networks (NNs) for enhanced learning and control.

Main Methods:

• Formulated decentralized optimal control for massive MASs as an MFG problem.
• Developed a novel actor-critic-mass (ACM) structure utilizing self-organizing NNs.
• Each agent employs three NNs: mass NN (solves Fokker-Planck-Kolmogorov equation), critic NN (solves Hamilton-Jacobian-Bellman equation), and actor NN (computes decentralized optimal control).
• Integrated self-organizing NNs to dynamically adjust network architecture based on learning performance and computational cost.

Main Results:

• The proposed ACM structure effectively learns the overall system behavior and optimal cost functions.
• Decentralized optimal control is accurately estimated, overcoming the need to solve coupled HJB and FPK equations simultaneously in real-time.
• Self-organizing NNs reduced computational complexity while maintaining control performance.
• Numerical simulations validated the effectiveness of the developed decentralized adaptive optimal control schemes.

Conclusions:

• The integration of MFG theory and self-organizing NNs provides an effective solution for decentralized optimal control in large-scale MASs.
• The developed ACM structure offers a computationally efficient and adaptive approach to handle complex, uncertain dynamics in massive agent populations.
• This work demonstrates a significant advancement in controlling complex systems by breaking the curse of dimensionality inherent in traditional methods.