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

IEEE Transactions on Cybernetics
Zejian Zhou, Hao Xu

Abstract

In this article, a decentralized adaptive optimal controller based on the emerging mean-field game (MFG) and self-organizing neural networks (NNs) has been developed for multiagent systems (MASs) with a large population and uncertain dynamics. This design can effectively break the ``curse of dimensionality'' and reduce the computational complexity by appropriately integrating emerging MFG theory with self-organizing NNs-based reinforcement learning techniques. First, the decentralized optimal control for massive MASs has been formulated into an MFG. To unfold the MFG, the coupled Hamilton-Jacobian-Bellman (HJB) equation and Fokker-Planck-Kolmogorov (FPK) equation needed to be solved simultaneously, which is challenging in real time. Therefore, a novel actor-critic-mass (ACM) structure has been developed along with self-organizing NNs subsequently. In the developed ACM structure, each agent has three NNs, including: 1) mass NN learning the mass MAS's overall behavior via online estimating the solution of the FPK equation; 2) critic NN obtaining the optimal cost function through learning the HJB equation solution along with time; and 3) actor NN estimating the decentralized optimal control by using the critic and mass NNs along w...Continue Reading

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