Networked Control and Mean Field Problems Under Diagonal Dominance: Decentralized and Social Optimality

In this article, we employ an input-output approach to expand the study of cooperative multi-agent control and optimization problems characterized by mean-field interactions that admit decentralized and selfish solutions. The setting involves $n$ independent agents that interact solely through a shared cost function, which penalizes deviations of each agent from the group's average collective behavior. Building on our earlier results established for homogeneous agents, we extend the framework to nonidentical agents and show that, under a diagonal dominant interaction of the collective dynamics, with bounded local open-loop dynamics, the optimal controller for $H_\infty$ and $H_2$ norm minimization remains decentralized and selfish in the limit as the number of agents $n$ grows to infinity.