Robust model predictive control for constrained linear system based on a sliding mode disturbance observer

For perturbed continuous-time systems, this paper proposes a robust model predictive control (RMPC) strategy for the regulation problem, exploiting a sliding mode disturbance observer. The main advantage is that it effectively enables the RMPC to be designed based on a model with reduced uncertainties. The proposed sliding mode observer (SMO) is finite-time convergent allowing the estimation error of the additive disturbance to be explicitly bounded by a predictable and decreasing limit. Due to the compensation of the estimated disturbance, the uncertainty that the RMPC has to handle is reduced from the original disturbance to the estimation error of the disturbance. This ensures all the admissible state trajectories are limited within a shrinking neighborhood of the origin and the steady-state error is therefore reduced. Simulation results show the effectiveness of the proposed method.