  Model Predictive Control (MPC) formulations are typically built on the
requirement that a feasible reference trajectory is available. In practical
settings, however, references that are infeasible with respect to the system
dynamics are used for convenience. In this paper, we prove under which
conditions an MPC formulation is Input-to-State Stable~(ISS) in closed-loop
when an infeasible reference is used, and that with proper terminal conditions,
asymptotic stability towards an optimal reference may be achieved. We
illustrate the theoretical results with a four-dimensional robotic joint
example.
