Constrained receding horizon controllers are often designed to regulate the system state
about some desired set-point subject to input constraints. This paper presents a class of
receding horizon controllers which force the inputs to lie inside the constraint set by
including a so-called `recentred barrier function'. The significance of such a
controller is that hard constraints are replaced with penalty type soft constraints. This
results in a control law that `backs off' near constraint boundaries. The degree to
which this backing-off occurs, is directly related to the parameter value that
characterises the class of controllers. For each parameter value there is a corresponding
unconstrained minimisation problem. The associated control law is obtained in the
standard manner by solving this problem at each time interval and applying the first
control move to the system. This method is applicable to general convex objective
functions with convex inequality constraints. We illustrate this idea by way of an example
application to linear discrete-time plant models with linear and convex quadratic static
input constraints.