This work presents a stochastic tube-based model predictive control framework that guarantees hard input constraint satisfaction for linear systems subject to unbounded additive disturbances. The approach relies on a structured design of probabilistic reachable sets that explicitly incorporates actuator saturation into the error dynamics and bounds the resulting nonlinearity within a convex embedding. The proposed controller retains the computational efficiency and structural advantages of stochastic tube-based approaches while ensuring state chance constraint satisfaction alongside hard input limits. Recursive feasibility and mean-square stability are established for our scheme, and a numerical example illustrates its effectiveness.
@article{arxiv.2602.19867,
title = {A Stochastic Tube-Based MPC Framework with Hard Input Constraints},
author = {Carlo Karam and Matteo Tacchi and Mirko Fiacchini},
journal= {arXiv preprint arXiv:2602.19867},
year = {2026}
}