  The main benefit of model predictive control (MPC) is its ability to steer
the system to a given reference without violating the constraints while
minimizing some objective. Furthermore, a suitably designed MPC controller
guarantees asymptotic stability of the closed-loop system to the given
reference as long as its optimization problem is feasible at the initial state
of the system. Therefore, one of the limitations of classical MPC is that
changing the reference may lead to an unfeasible MPC problem. Furthermore, due
to a lack of deep knowledge of the system, it is possible for the user to
provide a desired reference that is unfeasible or non-attainable for the MPC
controller, leading to the same problem. This chapter summarizes MPC
formulations recently proposed that have been designed to address these issues.
In particular, thanks to the addition of an artificial reference as decision
variable, the formulations achieve asymptotic stability and recursive
feasibility guarantees regardless of the reference provided by the user, even
if it is changed online or if it violates the system constraints. We show a
recent formulation which extends this idea, achieving better performance and
larger domains of attraction when working with small prediction horizons.
Additional benefits of these formulations, when compared to classical MPC, are
also discussed and highlighted with illustrative examples.
