Minimal Conjunctive Normal Expression of Continuous Piecewise Affine Functions

被引：3
|
作者：
Xu, Jun [1 ,2 ]
van den Boom, Ton J. J. [2 ]
De Schutter, Bart [2 ]
Luo, Xiong-Lin [1 ]
机构：
[1] China Univ Petr, Dept Automat, Beijing 102249, Peoples R China
[2] Delft Univ Technol, Delft Ctr Syst & Control, NL-2628 CD Delft, Netherlands
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2016年 / 61卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Conjunctive normal expression; continuous piecewise affine; minimal expression; NONLINEAR DYNAMICAL-SYSTEMS; MODEL-PREDICTIVE CONTROL; LINEAR REPRESENTATION; HINGING HYPERPLANES; COMPLEXITY; APPROXIMATION; REGRESSION; MPC;
D O I：
10.1109/TAC.2015.2465212
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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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页码：1340 / 1345
页数：6
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