Solving A Class of Mean-Field LQG Problems

TL;DR

This paper addresses a specific class of mean-field LQG problems, deriving explicit solutions and Riccati systems, with extensions to partial observation controls, advancing the theoretical understanding of these stochastic control problems.

Contribution

It provides explicit solutions and Riccati systems for a class of mean-field LQG problems, including extensions to partial observation scenarios.

Findings

Explicit solutions for mean-field LQG problems derived.

Riccati systems obtained by solving master equations.

Extensions to control problems with partial observations included.

Abstract

In this work, we study a class of mean-field linear quadratic Gaussian (LQG) problems. Under suitable conditions, explicit solutions of the distribution-dependent optimal control problems are obtained. Riccati systems are derived by directly solving the associated master equations. Some extensions on controls with partial observations are also considered.