# Mean Field Linear Quadratic Control: Uniform Stabilization and Social Optimality

arXiv: https://arxiv.org/abs/2002.12363 · HTML: https://mlsanity.com/paper/2002.12363/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2020.

## Built on by (most cited first, 3 of 3)

- [Mean Field LQG Social Optimization: A Reinforcement Learning Approach](https://mlsanity.com/paper/2410.15119/) (2024)
- [Reinforcement Learning for Discrete-time LQG Mean Field Social Control Problems with Unknown Dynamics](https://mlsanity.com/paper/2507.01420/) (2025)
- [Decentralized Strategies for Finite Population LQG Social Control: A Reinforcement Learning Approach](https://mlsanity.com/paper/2608.30244/) (2026)

## Abstract (arXiv)

This paper is concerned with uniform stabilization and social optimality for general mean field linear quadratic control systems, where subsystems are coupled via individual dynamics and costs, and the state weight is not assumed with the definiteness condition. For the finite-horizon problem, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback-type control by decoupling the FBSDEs. For the infinite-horizon problem, by using solutions to two Riccati equations, we design a set of decentralized control laws, which is further proved to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems in different cases, respectively. Finally, the proposed decentralized controls are compared to the asymptotic optimal strategies in previous works.