First Results on Turnpike Bounds for Stabilizing Horizons in NMPC. Issue 6 (2021) - Pan, Guanru; Stomberg, Gösta; Engelmann, Alexander; Faulwasser, Timm
Abstract: The stability analysis of NMPC schemes has seen significant progress in recent years, which includes schemes with and without terminal ingredients such as penalties and constraints. In the context of economic MPC, turnpike properties, which are closely related to dissipativity properties of the underlying optimal control problem, have enabled novel insights on stability conditions. In the present note, we show that turnpike properties naturally enable to bound the required stabilizing horizon length in MPC. The main idea is to define the turnpike with respect to a level-set of the terminal penalty. This way we derive a bound on the stabilizing horizon which guarantees that a terminal constraint is satisfied without being explicitly stated in the underlying optimal control problem. A numerical example indicates that if the terminal set is not too small, the horizon bound is not overly conservative.