基于浸入与不变原理的分数阶HR神经元同步控制

王琦; 王聪; 马萍; 张绍华

doi:10.13568/j.cnki.651094.651316.2023.01.18.0001

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基于浸入与不变原理的分数阶HR神经元同步控制

工程技术 | 更新时间：2026-01-21

- 基于浸入与不变原理的分数阶HR神经元同步控制
- 基于浸入与不变原理的分数阶HR神经元同步控制
- 新疆大学学报（自然科学版中英文） 2023年40卷第5期页码：630-640
- 作者机构：
  
  新疆大学电气工程学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金“复杂数据特征下风电传动系统故障诊断研究”（52065064）,“新能源电力系统的随机动力学分析与控制研究”（52267010）;新疆维吾尔自治区自然科学基金“复杂环境下高维电力系统混合动力学行为分析与控制研究”（2022D01C367）,“风电系统混沌振荡识别定位、耦合交互传播机理及抑制策略研究”（2022D01E33）
- DOI：10.13568/j.cnki.651094.651316.2023.01.18.0001
  中图分类号： Q189
- 纸质出版：2023
- 稿件说明：
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[1]王琦,王聪,马萍,等.基于浸入与不变原理的分数阶HR神经元同步控制[J].新疆大学学报(自然科学版)(中英文),2023,40(05):630-640.
[1]王琦,王聪,马萍,等.基于浸入与不变原理的分数阶HR神经元同步控制[J].新疆大学学报(自然科学版)(中英文),2023,40(05):630-640. DOI： 10.13568/j.cnki.651094.651316.2023.01.18.0001.

DOI：10.13568/j.cnki.651094.651316.2023.01.18.0001.

摘要

针对驱动-响应分数阶Hindmarsh-Rose(HR)神经元系统的同步问题，提出了一种基于浸入与不变原理的自适应分段滑模同步方案．首先，建立分数阶HR神经元模型并简要分析系统的动力学行为；其次，结合传统趋近律和饱和函数提出新型分段滑模趋近律来设计滑模控制器，接着引入浸入与不变理论建立不变流形并选取自适应律对系统内部不确定性和外部扰动进行估计，保证了流形的吸引性与不变性，并通过Lyapunov稳定性理论对所提方案进行稳定性证明；最后，通过数值仿真研究表明所提方案能使神经元系统达到完全同步，且明显减轻抖振现象，验证了所提方案的有效性与优越性．

Abstract

Aiming at the synchronization problem of drive-response fractional-order Hindmarsh-Rose(HR) neuron system

an adaptive segmented sliding mode synchronization scheme based on the principle of immersion and invariance is proposed. Firstly

a fractional-order HR neuron model is established and the dynamical behavior of the system is briefly analyzed; Secondly

a new piecewise sliding mode reaching law is proposed in combination with the traditional reaching law and saturation function to design a sliding mode controller

and then the immersion and invariance theory is introduced to establish the invariant manifold and select the adaptive law to estimate the internal uncertainty and external disturbance of the system

ensuring the attractiveness and invariance of the manifold

which ensures the attractiveness and invariance of the manifold

and proves the stability of the proposed scheme through the Lyapunov stability theory; Finally

numerical simulation studies show that the proposed scheme can achieve complete synchronization of the neuron system and significantly reduce the chattering phenomenon

which verifies the effectiveness and superiority of the proposed scheme.

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references

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