  Normals with unknown variance (NUV) can represent many useful priors
including $L_p$ norms and other sparsifying priors, and they blend well with
linear-Gaussian models and Gaussian message passing algorithms. In this paper,
we elaborate on recently proposed discretizing NUV priors, and we propose new
NUV representations of half-space constraints and box constraints. We then
demonstrate the use of such NUV representations with exemplary applications in
model predictive control, with a variety of constraints on the input, the
output, or the internal stateof the controlled system. In such applications,
the computations boil down to iterations of Kalman-type forward-backward
recursions, with a complexity (per iteration) that is linear in the planning
horizon. In consequence, this approach can handle long planning horizons, which
distinguishes it from the prior art. For nonconvex constraints, this approach
has no claim to optimality, but it is empirically very effective.
