  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.
