Irredundant lattice lattice representations of continuous piecewise affine functions

被引：18

作者：

Xu, Jun ^{[1
,2
]}

van den Boom, Ton J. J. ^{[2
]}

De Schutter, Bart ^{[2
]}

Wang, Shuning ^{[3
,4
]}

机构：

[1] China Univ Petr, Dept Automat, Beijing, Peoples R China

[2] Delft Univ Technol, Delft Ctr Syst & Control, NL-2600 AA Delft, Netherlands

[3] Tsinghua Univ, Dept Automat, Beijing 100084, Peoples R China

[4] TNList, Beijing, Peoples R China

来源：

AUTOMATICA | 2016年 / 70卷

基金：

中国国家自然科学基金;

关键词：

Piecewise affine function; Irredundant representation; Lattice representation; HINGING HYPERPLANES; MPC;

D O I：

10.1016/j.automatica.2016.03.018

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：109 / 120

页数：12

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