Reference
J. Xu,
T. J. J. van den Boom, B. De
Schutter, and X.-L. Luo, "Minimal conjunctive normal expression of continuous
piecewise affine functions,"
IEEE Transactions on Automatic
Control, vol. 61, no. 5, pp. 1340-1345, May 2016.
Abstract
Continuous piecewise affine (PWA) functions arise in many aspects of control.
For this kind of function, we propose the minimal conjunctive normal expression
(CNE). The CNE can be expressed as the minimum of a collection of terms, each
of which is the maximum of a set of affine functions. The minimal CNE is
defined to contain the smallest number of parameters. Analogous to Boolean
algebra, we propose implicants and prime implicants for continuous PWA
functions. After obtaining all prime implicants, the problem of finding minimal
CNEs can then be cast as a binary programming problem. A sharp bound on the
number of boolean variables in the binary programming problem is given. In two
worked examples, minimal CNEs are derived for given continuous PWA functions.
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BibTeX
@article{Xuvan:15-018,
author = {Xu, Jun and van den Boom, Ton J. J. and De Schutter, Bart and
Luo, Xiong-Lin},
title = {Minimal Conjunctive Normal Expression of Continuous Piecewise
Affine Functions},
journal = {IEEE Transactions on Automatic Control},
volume = {61},
number = {5},
pages = {1340--1345},
month = may,
year = {2016}
}