非线性抛物型分布参数系统的模糊迭代学习控制

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

Fuzzy Sets and Systems Pub Date : 2025-09-22 DOI:10.1016/j.fss.2025.109603

Xisheng Dai , Yanxue Wang , Senping Tian , Yangquan Chen , Zhijia Zhao

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引用次数: 0

摘要

研究了一类非线性抛物型分布参数系统的模糊迭代学习控制。提出了一种参数不确定的Takagi-Sugeno模糊DPS模型来近似非线性DPS。在此模型的基础上，设计了一种与隶属函数相关的模糊p型ILC算法，该算法可以根据系统输出误差调整学习增益。此外，该算法的模糊学习增益可以通过求解线性矩阵不等式（LMI）得到。通过构造Lyapunov函数，证明了系统在l2范数方面的跟踪误差收敛于零，同时也证明了输入误差单调收敛。最后，通过两个数值仿真验证了算法的有效性。

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Fuzzy iterative learning control for nonlinear parabolic distributed parameter systems

This study investigates fuzzy iterative learning control (ILC) for a class of nonlinear parabolic distributed parameter system (DPS). A Takagi-Sugeno (T-S) fuzzy DPS model with parameter uncertainty is proposed to approximate the nonlinear DPS. Based on this model, a fuzzy p-type ILC algorithm related to membership function is designed, which can adjust learning gain according to the system output error. Moreover, the fuzzy learning gain of this algorithm can be obtained by solving linear matrix inequality (LMI). By constructing a Lyapunov function, the system's tracking error in terms of

L^{2}

-norm is proven to converge to zero, while input error is proved monotonically convergent as well. Finally, the effectiveness of the algorithm is verified by two numerical simulations.

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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.