Model predictive control with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e299" altimg="si3.svg"> <mml:mi>λ</mml:mi> </mml:math> –contractive terminal sets

This article presents a novel model predictive control formulation for discrete-time linear systems subject to polyhedral state and control constraints. The proposed model predictive control replaces the fixed, time-invariant terminal set of standard model predictive control with a time-varying strategy: it initiates with a λ –contractive set, shrinks by a factor 0 ≤ λ < 1 at each time step, and then transitions to a conventional positively invariant terminal set based on a strategically designed switching condition. The proposed model predictive control also guarantees sequential positive invariance and uniform exponential stability properties of the controlled dynamics, while potentially achieving infinite horizon optimality. Most importantly, the resulting domain of attraction is significantly larger than that achieved by standard model predictive control.