Barrier regulator design using polyhedral predictive control

We consider the design of a barrier regulator - a special regulator, which tries to minimize the effect of state-space constraints violation in dynamical systems, creating a soft barrier in their state space. We employ a time-suboptimal predictive control strategy for discrete-time linear systems based on the minimization of a polyhedral distance function. Computationally, our approach reduces to the on-line solution of linear programming problems.