脉冲模糊神经网络的定/预定义时间稳定性：具有不定导数的Lyapunov方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-12-18 DOI:10.1016/j.cnsns.2024.108542

Luke Li, Qintao Gan, Ruihong Li, Qiaokun Kang, Huaiqin Wu

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引用次数: 0

摘要

研究了脉冲模糊神经网络的定/预定义时间稳定性问题。在Filippov解的框架下，利用Lyapunov方法首次建立了一些较为全面的不连续脉冲系统的FXTS/PTS定理。与大多数现有结果要求Lyapunov函数（LF）为负定或半负定相比，Lyapunov方法的独特之处在于LF的导数具有不确定性。此外，本文还特别考虑了具有时变脉冲强度的更一般的脉冲效应。然后利用所得到的FXTS/PTS定理，通过制定不同的控制策略来处理脉冲模糊神经网络的FXTS/PTS问题。给出了两个数值模拟来说明所得结果的有效性。

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Fixed-/predefined-time stability of impulsive fuzzy neural networks: Lyapunov method with indefinite derivative

In this article, the fixed-/predefined-time stability (FXTS/PTS) problems of impulsive fuzzy neural networks are concerned. Under the framework of Filippov solution, some more comprehensive FXTS/PTS theorems of discontinuous impulsive systems are first established by employing the Lyapunov method. Compared to most existing results, which require the Lyapunov function (LF) to be negative or semi-negative definite, the unique novelty of the Lyapunov method lies in the derivative of the LF possessing indefiniteness. Besides, more general impulse effects with time-varying impulse strength are especially considered in this article. Then the obtained FXTS/PTS theorems are further utilized to deal with the FXTS/PTS problems of impulsive fuzzy neural networks by developing different control strategies. Two numerical simulations are proposed to illustrate the effectiveness of the achieved results.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.