Definition of the HOSVD based canonical form of polytopic dynamic models
Definition of the HOSVD based canonical form of polytopic dynamic models
复制标题
基于 HOSVD 的多面动态模型规范形式的定义
DOI：
10.1109/icmech.2006.252604
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Y. Yam
中科院分区：
文献类型：
--
作者：
P. Baranyi;L. Szeidl;P. Várlaki;Y. Yam
本文的主要目的是介绍如何将张量HOSVD的概念推广到TP（张量积）动力学模型中，即如何定义和生成线性变参数（LPV）动力学模型的“类HOSVD”分解。我们称这种分解为基于HOSVD的TP模型的标准形式或多面体模型形式。提出了基于TP模型转换的控制器设计方法学中这种分解的核心思想和基本概念。本文的新奇在于提出了这一概念的数学背景。本文展示了收敛定理如何TP模型变换是能够重建这个HOSVD为基础的规范形式的数值。定理的证明是冗长的，因此它们被省略了。文中还给出了数值算例，说明了数值重构的适用性、有效性和一致性
The main objective of the paper is to introduce how the concept of tensor HOSVD can be carried over to the TP (tensor product) dynamic models, namely, how we can define and generate the "HOSVD like" decomposition of linear parameter varying (LPV) dynamic models. We term this decomposition as HOSVD based canonical form of TP model or polytopic model form. The key idea and the basic concept of this decomposition was proposed with the TP model transformation based control design methodology. The novelty of this paper is to present the mathematical background of this concept. The paper shows convergency theorems how the TP model transformation is capable of reconstructing this HOSVD based canonical form numerically. The proofs of the theorems are lengthy, therefore they are omitted. The paper also presents numerical examples to show the applicability, efficiency and uniformity of the numerical reconstruction