Reference:
J. Xu,
T.J.J. van den Boom,
B. De Schutter, and
S. Wang,
"Irredundant lattice representations of continuous piecewise affine
functions," Automatica, vol. 70, pp. 109-120, Aug. 2016.
Abstract:
In this paper, we revisit the full lattice representation of
continuous piecewise affine (PWA) functions and give a formal proof of
its representation ability. Based on this, we derive the irredundant
lattice PWA representations through removal of redundant terms and
literals. Necessary and sufficient conditions for irredundancy are
proposed. Besides, we explain how to remove terms and literals in
order to ensure irredundancy. An algorithm is given to obtain an
irredundant lattice PWA representation. In the worked examples, the
irredundant lattice PWA representations are used to express the
optimal solution of explicit model predictive control problems, and
the results turn out to be much more compact than those given by a
state-of-the-art algorithm.