  The stochastic linear-quadratic regulator problem subject to Gaussian
disturbances is well known and usually addressed via a moment-based
reformulation. Here, we leverage polynomial chaos expansions, which model
random variables via series expansions in a suitable $\mathcal{L}^2$
probability space, to tackle the non-Gaussian case. We present the optimal
solutions for finite and infinite horizons. Moreover, we quantify the
truncation error and we analyze the infinite-horizon asymptotics. We show that
the limit of the optimal trajectory is the unique solution to a stationary
optimization problem in the sense of probability measures. A numerical example
illustrates our findings.
