**Reference:**

J. Xu,
T.J.J. van den Boom,
B. De Schutter, and
X. 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.

Online version of the paper

Corresponding technical report: pdf file (148 KB)

@article{Xuvan:15-018,

author={J. Xu and T.J.J. van den Boom and B. {D}e Schutter and X. Luo},

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},

doi={10.1109/TAC.2015.2465212}

}

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