Conditions for which MPC fails to converge to the correct target

This paper considers the efficacy of disturbance models for ensuring offset free tracking and optimum steady-state target selection within linear model predictive control (MPC). Previously published methods for steady-state target determination can address model error, disturbances, and output target changes when the desired steady state is unconstrained, but may fail when there are active constraints. This paper focuses on scenarios where the most desirable target is unreachable, thus some constraints are active in steady state. Examples are given showing that the resulting feasible steady-state target can converge to a point which is not as close as possible to the true target. These failures have not been widely discussed in the literature. From the closed-loop behavior, hypotheses are put forward as necessary conditions for offset-free control. These hypotheses are then investigated through the use of Karush-Kuhn- Tucker (KKT) conditions of optimality