Risk-Constrained Control of Mean-Field Linear Quadratic Systems

TL;DR

This paper develops a risk-constrained control framework for mean-field linear quadratic systems, ensuring safety in the presence of risky events while maintaining scalability with many players.

Contribution

It introduces a novel risk-constrained LQ control method for mean-field systems with an affine controller structure and a scalable solution independent of the number of players.

Findings

Optimal controller is affine with risk control term

Solution is independent of the number of players

Simulations verify theoretical results

Abstract

The risk-neutral LQR controller is optimal for stochastic linear dynamical systems. However, the classical optimal controller performs inefficiently in the presence of low-probability yet statistically significant (risky) events. The present research focuses on infinite-horizon risk-constrained linear quadratic regulators in a mean-field setting. We address the risk constraint by bounding the cumulative one-stage variance of the state penalty of all players. It is shown that the optimal controller is affine in the state of each player with an additive term that controls the risk constraint. In addition, we propose a solution independent of the number of players. Finally, simulations are presented to verify the theoretical findings.