Convex Lifting: Theory and Control Applications
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.
Origin : Files produced by the author(s)
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