  We formulate and solve an optimal control problem with cooperative,
mean-field coupled linear-quadratic subsystems and additional risk-aware costs
depending on the covariance and skew of the disturbance. This problem
quantifies the variability of the subsystem state energy rather than merely its
expectation. In contrast to related work, we develop an alternative approach
that illuminates a family of matrices with many analytical properties, which
are useful for effectively extracting the mean-field coupled solution from a
standard LQR solution.
