Sequential Multi-Stage and Tube-based Robust MPC for Constrained Linear Systems with Multiplicative Uncertainty

Robust MPC algorithms using a multi-stage approach exhibit low levels of conservatism but suffer from an exponential growth of complexity with the prediction horizon. This may be an issue if long prediction horizons are required to achieve performance goals. In contrast, tube-based algorithms have a linear growth of computational complexity with the prediction horizon but show small domains of attraction. This work provides a method for a trade-off between the two approaches. A multi-stage approach is used during the first part of the prediction horizon, while a tube-based approach is employed for the remaining part. Stability and recursive feasibility are guaranteed for the algorithm and the performance of the approach is validated with numerical examples.