Model Predictive Control

44 3 Polyhedra, Polytopes and Simplices
the number of possible polyhedral combinations for merging explodes. As most of
these unions are not convex or even not connected and thus cannot be merged,
trying all combinations using standard techniques based on linear programming
(LP) is prohibitive. Furthermore, our objective here is not only to reduce the
number of polyhedra but rather to find the minimal and thus optimal number of
disjoint polyhedra. This problem is known to be N P-hard. In [109] more details
on the solutions of the three posed problems can be found.