Zonotope-Based Elastic Tube Model Predictive Control

Abstract

Tube-based Model Predictive Control (MPC) is a widely adopted robust control framework for constrained linear systems under additive disturbance. The paper is focused on reducing the numerical complexity associated with the tube parameterization, described as a sequence of elastically-scaled zonotopic sets. A new class of scaled-zonotope inclusion conditions is proposed, alleviating the need for a priori specification of certain set-containment constraints and achieving significant reductions in complexity. A comprehensive complexity analysis is provided for both the polyhedral and the zonotopic setting, illustrating the trade-off between an enlarged domain of attraction and the required computational effort. The proposed approach is validated through extensive numerical experiments.