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.
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BibTeX
@article{Xuvan:15-017,
author = {Xu, Jun and van den Boom, Ton J. J. and De Schutter, Bart and
Wang, Shuning},
title = {Irredundant Lattice Representations of Continuous Piecewise
Affine Functions},
journal = {Automatica},
volume = {70},
pages = {109--120},
month = aug,
year = {2016}
}