TY - JOUR
T1 - Irredundant lattice representations of continuous piecewise affine functions
AU - Xu, Jun
AU - van den Boom, Ton
AU - De Schutter, Bart
AU - Wang, S
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Piecewise affine function
KW - Irredundant representation
KW - Lattice representation
U2 - 10.1016/j.automatica.2016.03.018
DO - 10.1016/j.automatica.2016.03.018
M3 - Article
SN - 0005-1098
VL - 70
SP - 109
EP - 120
JO - Automatica
JF - Automatica
ER -