Model predictive control for tracking with implicit invariant sets

This paper presents a model predictive control (MPC) technique for tracking with implicit terminal components. The controller formulation includes an artificial setpoint as decision variable, and the terminal constraint is defined implicitly for an augmented system that depends on the latter. In this respect, instead of computing an invariant terminal set, we consider an extended prediction horizon whose length can be bounded simply by solving LPs. This approach overcomes size-related limitations associated with the operations needed for computing invariant sets, also simplifying the offline MPC design. The proposed controller is able to drive large systems to admissible setpoints while guaranteeing recursive feasibility and convergence. Finally, the method is illustrated by an academic example, a mass–spring–damper system of variable-size and a more realistic case study of a drone.