An improved control law for TS fuzzy models: Less conservative LMI conditions by using membership functions derivative

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-05-13 DOI:10.1016/j.fss.2025.109455

Leonardo Amaral Mozelli, Victor Costa da Silva Campos

引用次数: 0

Abstract

This note proposes an enhanced version of the Parallel Distributed Compensation (PDC) for Takagi-Sugeno (TS) fuzzy models. Our approach involves two control terms based on state feedback. The first term is a convex combination of linear gains weighted by the normalized membership grade, as in traditional PDC. The second term is the main contribution and introduces linear gains weighted by the time derivatives of the membership functions. We formulate the design conditions as Linear Matrix Inequalities (LMIs), solvable through numerical optimization tools. Numerical examples illustrate the advantages of our proposal, which encompasses the traditional PDC as a special case.

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一种改进的TS模糊模型控制律：基于隶属函数导数的更少保守LMI条件

本文针对Takagi-Sugeno （TS）模糊模型提出了一种改进的并行分布式补偿（PDC）方法。我们的方法包含两个基于状态反馈的控制项。第一项是由归一化隶属度加权的线性增益的凸组合，与传统PDC一样。第二项是主要贡献，并引入了由隶属函数的时间导数加权的线性增益。我们将设计条件表述为线性矩阵不等式（lmi），可通过数值优化工具求解。数值例子说明了我们的建议的优点，其中包括传统PDC作为一个特殊的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.