Irredundant lattice representations of continuous piecewise affine functions

Jun Xu; Ton J.J. Van Den Boom; Bart De Schutter; Shuning Wang

doi:10.1016/j.automatica.2016.03.018

Irredundant lattice representations of continuous piecewise affine functions

Jun Xu
, Ton J.J. Van Den Boom
, Bart De Schutter
, Shuning Wang

China University of Petroleum - Beijing
Delft University of Technology
Tsinghua University

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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.

Original language	English
Pages (from-to)	109-120
Number of pages	12
Journal	Automatica
Volume	70
DOIs	https://doi.org/10.1016/j.automatica.2016.03.018
State	Published - 1 Aug 2016
Externally published	Yes

Keywords

Irredundant representation
Lattice representation
Piecewise affine function

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10.1016/j.automatica.2016.03.018

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title = "Irredundant lattice representations of continuous piecewise affine functions",

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.",

keywords = "Irredundant representation, Lattice representation, Piecewise affine function",

author = "Jun Xu and \{Van Den Boom\}, \{Ton J.J.\} and \{De Schutter\}, Bart and Shuning Wang",

year = "2016",

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T1 - Irredundant lattice representations of continuous piecewise affine functions

AU - Xu, Jun

AU - Van Den Boom, Ton J.J.

AU - De Schutter, Bart

AU - Wang, Shuning

PY - 2016/8/1

Y1 - 2016/8/1

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 - Irredundant representation

KW - Lattice representation

KW - Piecewise affine function

UR - https://www.scopus.com/pages/publications/84963684554

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DO - 10.1016/j.automatica.2016.03.018

M3 - 文章

AN - SCOPUS:84963684554

SN - 0005-1098

VL - 70

SP - 109

EP - 120

JO - Automatica

JF - Automatica

ER -

Irredundant lattice representations of continuous piecewise affine functions

Abstract

Keywords

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