Exploiting symmetries in tree-based combinatorial calculation of explicit linear MPC solutions

Symmetries of linear MPC problems are reflected in symmetries of their explicit solutions. We recently showed these symmetries also appear in the set of the active sets that define the explicit solution. Consequently, symmetries can be used to speed up algorithms for the calculation of the set of active sets. In this paper, we exploit symmetries to accelerate the approach from [1] by improving the exploration of the combinatorial tree of active sets. The reductions of the computational effort that can be achieved are illustrated and analyzed with two examples.