Efficient computation of RPI sets for tube-based robust MPC

We present a novel method for the computation of small RPI sets tailored for tube-based robust MPC. In the framework of robust MPC for linear systems with additive disturbances, RPI sets are used to guarantee robust constraint satisfaction (and robust stability) through constraint tightening. To minimize the tightening, small RPI sets are beneficial. Hence, classical approaches aim for ε-approximations of the minimal RPI set. Unfortunately, the computation of those approximations usually requires Minkowski sums that are numerically expensive. In contrast, our method avoids demanding Minkowski sums. Nevertheless, the resulting RPI sets lead to tightened constraints that are identical to those for ε-approximations of the minimal RPI set. The (simple) key observation underlying our approach is that the Pontryagin difference, that is instrumental for the constraint tightening, can lead to identical results for different subtrahend sets.