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Model Predictive Control (MPC) formulations are typically built on therequirement that a feasible reference trajectory is available. In practicalsettings, however, references that are infeasible with respect to the systemdynamics are used for convenience. In this paper, we prove under whichconditions an MPC formulation is Input-to-State Stable~(ISS) in closed-loopwhen an infeasible reference is used, and that with proper terminal conditions,asymptotic stability towards an optimal reference may be achieved. Weillustrate the theoretical results with a four-dimensional robotic jointexample.

Model Predictive Control with Infeasible Reference Trajectories