Tracking control for nonlinear systems with time-varying delay using the fuzzy preview repetitive control approach

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS Fuzzy Sets and Systems Pub Date : 2025-03-20 DOI:10.1016/j.fss.2025.109378

Li Li , Jiang Wu , Xiaohua Meng

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Abstract

This paper investigates an innovative technology for fuzzy preview repetitive control (FPRC) in nonlinear systems with time-varying delay and uncertainties using the Takagi-Sugeno (T-S) fuzzy model. The proposed FPRC strategy considers time-changing delays and previewable, periodic target signals. The controller integrates a fuzzy output feedback controller, a fuzzy preview controller, and a repetitive controller to address the tracking control problem of periodic target signals. The research constructs a T-S fuzzy augmented error system using the error system method and state augmentation technique. Subsequetnly, the FPRC design challenge is transformed into a feedback stabilization problem of the augmented error system. Empolying fuzzy Lyapunov function and linear matrix inequality (LMI) techniques, the study derives sufficient conditions for the asymptotic stability of the augmented error system in the form of a set of LMIs, presenting the design method of the FPRC law. The validity of the results is demonstrated through numerical simulations.

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使用模糊预览重复控制法对具有时变延迟的非线性系统进行跟踪控制

本文研究了一种基于Takagi-Sugeno （T-S）模糊模型的时变时滞和不确定性非线性系统模糊预览重复控制（FPRC）的创新技术。提出的FPRC策略考虑了时变延迟和可预览的周期性目标信号。该控制器集成了模糊输出反馈控制器、模糊预览控制器和重复控制器，解决了周期性目标信号的跟踪控制问题。利用误差系统方法和状态增广技术构建了T-S模糊增广误差系统。然后，将FPRC的设计挑战转化为增广误差系统的反馈镇定问题。利用模糊Lyapunov函数和线性矩阵不等式（LMI）技术，以LMI集合的形式推导出增广误差系统渐近稳定的充分条件，给出了FPRC律的设计方法。通过数值模拟验证了结果的有效性。

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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.