  This article is devoted to providing a review of mathematical formulations in
which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model
predictive control (SMPC). In the past decade, PCT has been shown to provide a
computationally tractable way to perform complete and accurate uncertainty
propagation through (smooth) nonlinear dynamic systems. As such, it represents
a very useful computational tool for accelerating the computations needed in
SMPC with time invariant uncertainties. It turns out that it can also be used
to reduce complexity of chance constraints, which are an important component of
SMPC. In this paper, we provide an overview of PCT and discuss how it can be
applied in such time invariant settings.
