Model Predictive Control with Infeasible Reference Trajectories

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.