Steady states and constraints in model predictive control

Studies on the theory of model predictive control include the assumption that the origin is in the interior of the feasible region (that is, the inequality constraints are not active at steady state). The reason for making this assumption is that without it one cannot guarantee feasibility of die control problem on the infinite horizon because of the finite horizon parameterization of the input with an unconstrained linear feedback law.. As demonstrated in this article, however; this assumption often does not hold in practice. A strategy for handling inequality constraints active at steady state is presented by projecting the system onto the active constraints under the finite horizon parameterization of the input, as well as an algorithm for constructing the optimal linear feedback law that constrains the system to the active constraints. Feasibility is obtained using output admissible sets. For the steady-state target calculation, we propose an algorithm utilizing exact penalties that treats systems in a unified fashion with more inputs than outputs and vice versa. Assuming the system is detectable, it is proven that the algorithm yields a unique steady-state target.