A Combined Multi-stage and Tube-based MPC Scheme for Constrained Linear Systems

Abstract

Abstract The multi-stage MPC approach models the evolution of state trajectories for different realizations of the uncertainty as a scenario tree and considers the availability of feedback information explicitly in the predictions and in the computation of the control moves. Since the structure of the feedback policy is not restricted, multi-stage MPC is less conservative when compared to approaches that use e.g. affine feedback policies. The advantages come at the cost of rapid growth in problem size with respect to the number of uncertainties and the prediction horizon. In this paper, we propose to use affine control policies for small disturbances and the multi-stage approach for large uncertainties to obtain a better trade-off between optimality and complexity than the existing robust MPC schemes. The proposed scheme mitigates the problem of the increase in problem complexity with respect to the number of uncertainties at the price of only a small loss of performance. We show that the proposed scheme is robustly exponentially stable and demonstrate its advantages for a CSTR example.