Robust Model Predictive Control with Time-varying Tubes

This paper focuses on the problem of robustly stabilizing uncertain discrete-time systems subject to bounded disturbanceS. The proposed tube-based model predictive controller ensures that all possible realizations of the state trajectory lie in the time-varying tubes so robust stability and satisfaction of the state and input constraints are guaranteed. The time-varying tubes are computed off-line so the on-line computational time is tractable. At each sampling time, the precomputed time-varying tubes are included in the optimal control problem as the constraints in the prediction horizon and only a quadratic programming problem is solved. In comparison to the algorithm that. calculates the time-varying tubes on-line, the proposed algorithm can achieve the same level of control performance while the on-line computational time is greatly reduced.