Model predictive control requires the minimization of a cost function at each control
step. Recently the authors have proposed controlling plants with input constraints by
including the constraints as a barrier with fixed weighting in the cost function. In effect
the constrained model predictive control problem then requires an unconstrained
nonlinear optimization at each control step. In particular, if the original cost function
(without constraints) is smooth and convex, then a class of controllers is generated for
the constrained problem where the cost to be minimized is also smooth and convex and
whose gradient is zero at the optimal solution. In this paper we show that the idea may
be straightforwardly generalised to plants with state constraints. We illustrate the idea
with a simulation of a plant with rate constraints on the actuators.