Fusing multiple time varying tubes for robust MPC

We consider robust tube based model predictive control of discrete time, constrained, linear systems subject to additive disturbances. Standard tube based approaches utilize as an auxiliary control law a single, fixed feedback/gain to counteract the effect of the future disturbances in the predictions. The fictive - never applied - control law allows to bound the error between the real state and the nominal predictions by so called tubes. The tube control law strongly influences the shape and size of the tube. Consequently, the choice of the gain has a major impact on the domain of attraction and the control performance of the overall controller. The objective of this work is to overcome these limitations by combining multiple tubes online, each determined by a different controller gain. This reduces the conservatism and improves the closed loop performance. The computational demand for the resulting control law increases only marginally, compared to the standard case. We establish constraint satisfaction, robust recursive feasibility and robust stability. Moreover extension to the case of varying disturbance bounds are discussed. The proposed approach and its benefits are illustrated using simulations.