Tube-based stochastic model predictive control with flexible state initialization

The robust model predictive control does not exploit the potentially existing statistical properties of system uncertainties, which may result in overly conservative control solutions. To address this issue, this paper proposes a novel approach of stochastic model predictive control, specifically tailored for linear time-invariant systems that are confronted with bounded additive uncertainties. The proposed method is established within the robust tube-based model predictive control framework, where chance constraints are transformed into deterministic ones. In particular, by leveraging the propagation characteristics of uncertainties, an algorithm of time-varying tube-based stochastic model predictive control is devised through computing tightened constraints along the prediction horizons. Furthermore, utilizing the infinite-horizon propagation property of uncertainties, a constant tube-based stochastic model predictive control method is derived by implementing conservatively constant tightened constraints throughout the entire prediction horizons. The feasibility and closed-loop stability results are rigorously developed, and a numerical example is provided to demonstrate the efficacy of the proposed method.