变分数阶Sprott-R混沌系统有限时间自适应滑模同步

Finite-Time Adaptive Sliding Mode Synchronization of Variable Fractional-Order Sprott-R Chaotic Systems

摘要

研究Sprott-R变分数阶混沌系统自适应滑模同步,根据变分数阶Lyapunov稳定性理论,采用有限时间同步相关结论,在一定的假设前提下,通过设计变分数阶有限时间自适应滑模控制器,得到Sprott-R变分数阶混沌系统的同步条件,并用MATLAB进行数值仿真,对结论进行验证.

Abstract

We studied adaptive sliding mode synchronization of variable fractional-order Sprott-R chaotic system. Based on variable fractional-order Lyapunov stability theory, we applied finite-time synchronization related conclusions and designed a variable fractional-order finite-time adaptive sliding mode controller to obtain the synchronization conditions of variable fractional-order Sprott-R chaotic system under certain assumptions. We then used MATLAB for number simulation to verify the conclusion.

关键词

变分数阶 / Sprott-R混沌系统 / 滑模同步

Key words

variable fractional-order / Sprott-R chaotic system / sliding mode synchronization

参考文献

[1] 曾繁鹏, 赖强, 赖聪. 忆阻Sprott-R混沌系统的复杂动态分析与电路实现[J]. 量子电子学报, 2024, 41(1):170-183.

[2] (Zeng F P, Lai Q, Lai C. Complex Dynamic Analysis and Circuit Realization of Memristive Sprott-R Chaotic System[J]. Chinese Journal of Quantum Electronics, 2024, 41(1): 170-183.)

[3] Song S, Zhang B Y, Song X N, et al. Fractional-Order Adaptive Neuro-Fuzzy Sliding Mode H_∞ Control for Fuzzy Singularly Perturbed Systems[J]. Journal of Franklin Institute, 2019, 356(10): 5027-5048.

[4] Sun Z Y, Dai Y Y, Chen C C. Global Fast Finite-Time Partial State Feedback Stabilization of High-Order Nonlinear Systems with Dynamic Uncertainties[J]. Information Sciences, 2019, 77(1): 219-236.

[5] Zhang Z, Zhang J, Cheng F Y, et al. A Novel Stability Criterion of Time-Varying Delay Fractional-Order Financial Systems Based a New Functional Transformation Lemma[J]. International Journal of Control, Automation and Systems, 2019, 17(4): 916-925.

[6] 毛北行, 王东晓. 不确定分数阶高维混沌系统的自适应滑模同步[J]. 电子学报, 2021, 49(4):775-780.

[7] (Mao B X, Wang D X. Self-adaptive Sliding Mode Synchronization of Uncertain Fractional-Order High-Dimension Chaotic Systems[J]. Acta Electronica Sinica, 2021, 49(4): 775-780.)

[8] 毛北行, 王东晓. 具有外扰和不确定项的分数阶非线性混沌系统的自适应滑模同步[J]. 吉林大学学报(理学版), 2020, 58(5):1237-1242.

[9] (Mao B X, Wang D X. Self-adaptive Sliding Mode Synchronization of Fractional-Order Nonlinear Chaotic System with Outer Disturbance and Uncertainty[J]. Journal of Jilin University (Science Edition), 2020, 58(5): 1237-1242.)

[10] 毛北行. 分数阶多混沌系统滑模同步两种方法的比较[J]. 电子学报, 2020, 48(11):2215-2219.

[11] (Mao B X. Two Methods Contrast of Sliding Mode Synchronization of Fractional-Order Multi-chaotic Systems[J]. Acta Electronica Sinica, 2020, 48(11): 2215-2219.)

[12] 毛北行, 王东晓. 金融不确定分数阶混沌系统滑模同步的3种控制方案[J]. 吉林大学学报(理学版), 2022, 60(5):1183-1188.

[13] (Mao B X, Wang D X. Three Control Schemes of Sliding Mode Synchronization of Financial Uncertain Fractional-Order Chaotic Systems[J]. Journal of Jilin University (Science Edition), 2022, 60(5): 1183-1188.)

[14] 周卫光, 章安, 郑永爱. 不相称分数阶Genesio-Tesi系统的有限时间自适应滑模同步[J]. 扬州大学学报(自然科学版), 2023, 26(3):50-55.

[15] (Zhou W G, Zhang A, Zheng Y A. Finite Time Adaptive Sliding Mode Synchronization of Incommensurate Fractional Order Genesio-Tesi Systems[J]. Journal of Yangzhou University (Natural Science Edition), 2023, 26(3): 50-55.)

[16] 毛北行, 王东晓. 分数阶永磁同步电机混沌系统自适应滑模同步[J]. 浙江大学学报(理学版), 2023, 50(5):564-568.

[17] (Mao B X, Wang D X. Self-adaptive Sliding Mode Synchronization of Fractional-Order Permanent Magnet Synchronization Motor Chaotic Systems[J]. Journal of Zhejiang University (Science Edition), 2023, 50(5): 564-568.)

[18] 黄燕萍. 一类线性变分数阶微分方程的数值解[J]. 玉林师范学院学报(自然科学), 2004, 45(3):11-15.

[19] (Huang Y P. Numerical Solutions of a Class of Linear Fractional Differential Equations with Variable Coefficients[J]. Journal of Yulin Normal University (Science Edition), 2004, 45(3): 11-15.)

[20] 章安. 变分数阶混沌系统同步控制研究[D]. 扬州: 扬州大学, 2024.

[21] (Zhang A. Research on Control of Synchronization of Variable Fractional Chaotic Systems[D]. Yangzhou: Yangzhou University, 2024.)

[22] 闫丽宏. 广义分数阶Sprott-C混沌系统的有限时间滑模同步[J]. 吉林大学学报(理学版), 2019, 57(4):940-945.

[23] (Yan L H. Finite-Time Sliding Mode Synchronization of Generalized Fractional-Order Sprott-C Chaotic Systems[J]. Journal of Jilin University (Science Edition), 2019, 57(4): 940-945.)

[24] 刘恒, 李生刚, 孙业国, 等. 带有未知非对称控制增益的不确定分数阶混沌系统自适应模糊混沌控制[J]. 物理学报, 2015, 64(7):128-136.

[25] (Liu H, Li S G, Sun Y G, et al. Adaptive Fuzzy Synchronization for Uncertain Fractional-Order Chaotic Systems with Unknown Non-symmetrical Control Gain[J]. Acta Physica Sinica, 2015, 64(7): 128-136.)

[26] Jiang J, Cao D, Chen H. Sliding Mode Control for a Class of Variable-Order Fractional Chaotic Systems[J]. Journal of the Franklin Institute, 2020, 357(15): 10127-10158.

[27] Bhat S P, Bernstein D S. Geometric Homogeneity with Applications to Finite-Time Stability[J]. Mathematics of Control Signals and Systems, 2005, 17(2): 101-127.

基金资助

国家自然科学基金(12401655)

河南省高等学校重点科研项目计划基础研究专项基金(24ZX008)

河南省自然科学基金(252300420350)