Distributed Control of Linear Quadratic Mean Field Social Systems with Heterogeneous Agents

TL;DR

This paper develops a distributed control framework for large-scale linear quadratic mean field systems with heterogeneous agents, utilizing network topology and mean field approximations to achieve asymptotic social optimality.

Contribution

It introduces a novel approach combining graph-based network modeling with mean field control to design distributed controllers for heterogeneous agent systems.

Findings

Distributed controllers are asymptotically socially optimal.

The approach effectively handles heterogeneous agent dynamics.

Controllers are derived using Riccati equations and mean field approximations.

Abstract

In this paper, we study the social optimality for mean field linear quadratic control systems following the direct approach, where subsystems are coupled via individual dynamics and costs according to a network topology. A graph is introduced to represent the network topology of the large-population system, where nodes represent subpopulations called clusters and edges represent communication relationship. By the direct approach, we first seek the optimal controller under centralized information structure, which characterized by a set of forward-backward stochastic differential equations. Then the feedback controller is obtained with the help of Riccat equations. Finally, we design the distributed controller with mean field approximations, which has the property of asymptotically social optimality.