Abstract : This paper presents the concept of convex lifting
which will be proven to enable significant implementation benefits
for the class of piecewise affine controllers. Accordingly, two
different algorithms to construct a convex lifting for a given
polyhedral/polytopic partition will be presented. These two algorithms
rely on either the vertex or the halfspace representation
of the related polyhedra. Also, we introduce an algorithm to
refine a polyhedral partition, which does not admit a convex
lifting, into a convexly liftable one. Furthermore, two different
schemes will be put forward to considerably reduce both the
memory footprint and the online evaluation effort, which play a
key role in implementation of piecewise affine controllers. Finally,
these results will be illustrated via numerical examples and a
complexity analysis.
