Finite-time convergence results in Model Predictive Control

Abstract

Asymptotic stability (convergence and $\epsilon-\delta$ stability) of invariant sets under model predictive control (MPC) strategies have been extensively studied in the last decades. Lyapunov theory is in some sense the common denominator of the different forms to achieve such results. However, the meaningful problem of the finite-time convergence (for a given fixed control horizon) has not received much attention in the literature (with some remarkable exceptions). In this work a novel set-based MPC that ensures finite-time convergence in a natural way is presented. The contractivity and non-empty interior conditions of the target set, the consideration of an appropriate input set and the continuity of the dynamic model are the main hypothesis to be made. An upper bound for the convergence time is also provided.