Improvement of controller design for positive polynomial fuzzy systems based on symbolic analysis and optimization of reduced-Order parameters of interval type-2 membership functions

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2026-06-15 Epub Date: 2026-02-18 DOI:10.1016/j.fss.2026.109836

Ziyu Wang , Meng Han , Yiming Han , Ge Guo , Zhengsong Wang

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引用次数: 0

Abstract

In this paper, the controller design of positive interval Type-2 polynomial fuzzy-model-based (PIT2PFMB) systems is investigated, where the PIT2PFMB open-loop system and the controller are permitted to employ distinct premise membership functions. While this premise mismatch enhances controller design flexibility, it introduces conservatism when analyzing stability via Lyapunov stability theory. To mitigate this conservatism, an advanced membership function dependent analysis method is proposed: type-reduction parameters are modeled as system symbolic variables, with their information, together with other information of membership functions, incorporated into the stability conditions. This approach expands the stability regions of the systems. During the type-reduction implementation of the interval Type-2 (IT2) fuzzy controller, the gradient descent approach is employed to optimize the embedded type-1 membership functions of the controllers, thereby improving the control performance. Simulation results will demonstrate the effectiveness of the proposed methodology in expanding the stability region and improving control performance.

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基于符号分析和区间2型隶属函数降阶参数优化的正多项式模糊系统控制器设计改进

本文研究了正区间2型多项式模糊模型（PIT2PFMB）系统的控制器设计，其中PIT2PFMB开环系统和控制器允许采用不同的前提隶属函数。虽然这种前提不匹配增强了控制器设计的灵活性，但在利用李雅普诺夫稳定性理论分析稳定性时引入了保守性。为了缓解这种保守性，提出了一种先进的隶属函数相关分析方法：将类型约简参数建模为系统符号变量，并将其信息与隶属函数的其他信息一起纳入稳定性条件。这种方法扩展了系统的稳定域。在区间Type-2 （IT2）模糊控制器的类型约简实现中，采用梯度下降法对控制器的嵌入式type-1隶属度函数进行优化，从而提高了控制性能。仿真结果将证明该方法在扩大稳定区域和提高控制性能方面的有效性。

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.