Large-Population Optimal Control with Mixed Agents: The Multi-Scale Analysis and Decentralized Control

We consider a large-population optimal control problem involving a major agent and a large number of minor agents. By starting with a centralized optimal control problem, we employ a re-scaling method to derive decentralized control laws. This re-scaling method is further used to obtain a tight upper bound of
$O (1/N)$
for the performance loss resulting from decentralized control. This improves upon known results of
$O (1/\sqrt{N})$
in the literature for similar models.