This thesis considers the use of barrier functions in the context of constrained model
predictive control (MPC). A new class of controller is developed by including a weighted
barrier function in the objective that ensures inequality constraints are satisfied. Fixing
the barrier weighting term to be some positive value – possibly much greater than zero
– has interesting effects on controller dynamics, particularly near constraint boundaries.
When the barrier weighting term is close to zero, the corresponding dynamic behaviour
resembles that of standard MPC. In fact standard MPC is subsumed within the new class
as a special limiting case; in this way, the new class may be seen as a generalisation
of standard MPC. Conditions are determined for the barrier such that correct steadystate
behaviour is guaranteed; a barrier satisfying these conditions is called a recentred
barrier and consequently the new controller class is called recentred barrier function MPC
(abbreviated as r-MPC). The barrier approach shares the same fundamental philosophy
as interior-point methods – a connection which is exploited throughout this thesis. For
example, interior-point geometry is exploited to show nominal closed-loop stability of
r-
MPC for the case of linear system models. Similarly, algorithms for solving the associated
optimisation problem can be developed in a natural manner. Indeed, the algorithms
developed in this thesis are modifications of existing interior-point algorithms; they also
maintain the polynomial complexity exhibited by the latter. The new controller class is
validated via a successful industrial application to edible oil refining. The industrial trials
demonstrate how the barrier weighting parameter can be interpreted as another tuning
parameter for the controller. Changing the weighting value has the effect of adjusting
controller caution near constraint boundaries.