A Stochastic Tube-Based MPC Framework with Hard Input Constraints

TL;DR

This paper introduces a stochastic tube-based MPC framework that guarantees hard input constraints and state chance constraints for linear systems with unbounded disturbances, combining probabilistic reachable sets with convex bounds.

Contribution

It presents a novel structured design of probabilistic reachable sets that explicitly incorporate actuator saturation, ensuring hard input constraints within a stochastic MPC framework.

Findings

Guarantees hard input constraint satisfaction.

Ensures state chance constraint satisfaction.

Proves recursive feasibility and mean-square stability.

Abstract

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.