A Stochastic Tube-Based MPC Framework with Hard Input Constraints
Carlo Karam, Matteo Tacchi, Mirko Fiacchini
TL;DR
This paper develops Saturation-Aware SMPC (SA-SMPC), a tractable tube-based MPC framework that guarantees hard input constraint satisfaction for linear systems under unbounded disturbances by explicitly modeling actuator saturation within the PRS construction. It embeds convex bounds of the saturated error dynamics into probabilistic reachable sets, enabling deterministic constraint tightening that preserves online tractability while enforcing state chance constraints. The authors establish recursive feasibility, state-chance satisfaction, and mean-square stability, and validate the approach on a discretized CSTR model, showing favorable trade-offs between performance and computation compared to affine disturbance-feedback and SOCP-based methods. The work offers a practical, scalable method for enforcing hard input limits in stochastic MPC and suggests future enhancements via moment-based certificates to reduce conservatism.
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.