Tube-enhanced multi-stage model predictive control for flexible robust control of constrained linear systems with additive and parametric uncertainties

The trade-off between optimality and complexity has been one of the most important challenges in the field of robust model predictive control (MPC). To address the challenge, we propose a flexible robust MPC scheme by synergizing the multi-stage and tube-based MPC approaches. The key idea is to exploit the nonconservatism of the multi-stage MPC and the simplicity of the tube-based MPC. The proposed scheme provides two options for the user to determine the trade-off depending on the application: the choice of the robust horizon and the classification of the uncertainties. Beyond the robust horizon, the branching of the scenario-tree employed in multi-stage MPC is avoided with the help of tubes. The growth of the problem size with respect to the number of uncertainties is reduced by handling small uncertainties via an invariant tube that can be computed offline. This results in linear growth of the problem size beyond the robust horizon and no growth of the problem size concerning small magnitude uncertainties. The proposed approach helps to achieve a desired trade-off between optimality and complexity compared to existing robust MPC approaches. We show that the proposed approach is robustly asymptotically stable. Its advantages are demonstrated for a CSTR example.