离散耦合复杂网络系统的稳定性分析
Stability Analysis of Discretely-Coupled Complex Networks Systems
DOI: 10.12677/pm.2024.146247, PDF,    科研立项经费支持
作者: 尉锐芳, 纪 楠*：华北理工大学理学院，河北 唐山
关键词: 复杂网络；脉冲控制；稳定性；时滞；Complex Network； Impulsive Control； Stability； Time-Delay
摘要: 以离散耦合复杂网络系统为研究对象，当系统遭受突然变化时，设计脉冲控制器，在控制器中添加时滞项和饱和两个约束条件，采用凸包分析法处理饱和项，并基于Lyapunov稳定性理论进一步推导出此系统在脉冲控制下的指数稳定性判据。最后，选择包含两个状态节点的系统进行数值仿真。对于原系统不稳定的情况，施加脉冲控制，而在原系统稳定的情况下，施加脉冲扰动，以验证所得稳定性判据的准确性与有效性。
Abstract: Taking discrete coupled complex network system as the research object, when the system is subjected to sudden changes, a pulse controller is designed, two constraints of delay term and saturation term are added to the controller, and the saturation term is processed by convex hull analysis method. Then, Lyapunov stability theory is employed to further derive the criterion for the stability of discrete-time coupled complex network systems under impulsive control. Finally, systems comprising two state nodes are selected for numerical simulation. For the case where the original system is unstable, impulsive control is applied, and for the case where the original system is stable, impulsive disturbances are applied to validate the effectiveness of the stability results obtained.
文章引用：尉锐芳, 纪楠. 离散耦合复杂网络系统的稳定性分析[J]. 理论数学, 2024, 14(6): 269-281. https://doi.org/10.12677/pm.2024.146247

参考文献

[1] 刘鹏辉, 琚贇, 高维星, 等. 基于强化学习的网络拥塞控制优化算法[J]. 电力科学与工程, 2023, 39(4): 20-27.
[2] 王立夫, 朱枫, 郭戈, 等. 基于负载系数的轨道交通网络控制站点辨识[J]. 控制与决策, 2020, 35(10): 2319-2328.
[3] Xu, C., Yang, X., Lu, J., Feng, J., Alsaadi, F.E. and Hayat, T. (2018) Finite-Time Synchronization of Networks via Quantized Intermittent Pinning Control. IEEE Transactions on Cybernetics, 48, 3021-3027. [Google Scholar] [CrossRef] [PubMed]
[4] Kumar, R., Kumar, U., Das, S., Qiu, J. and Lu, J. (2021) Effects of Heterogeneous Impulses on Synchronization of Complex-Valued Neural Networks with Mixed Time-Varying Delays. Information Sciences, 551, 228-244. [Google Scholar] [CrossRef] 
[5] Chen, X., Huang, T., Cao, J., Park, J.H. and Qiu, J. (2019) Finite-Time Multi-Switching Sliding Mode Synchronisation for Multiple Uncertain Complex Chaotic Systems with Network Transmission Mode. IET Control Theory & Applications, 13, 1246-1257. [Google Scholar] [CrossRef] 
[6] Wu, Y., Zhu, J. and Li, W. (2020) Intermittent Discrete Observation Control for Synchronization of Stochastic Neural Networks. IEEE Transactions on Cybernetics, 50, 2414-2424. [Google Scholar] [CrossRef] [PubMed]
[7] Zhang, X. and Li, C. (2020) Finite-Time Stability of Nonlinear Systems with State-Dependent Delayed Impulses. Nonlinear Dynamics, 102, 197-210. [Google Scholar] [CrossRef] 
[8] Liu, X., Chen, D. and Wang, Y. (2019) Distributed Impulsive Consensus of Nonlinear Multi-Agent Systems with Input Saturation. International Journal of Modern Physics C, 30, Article 1940001. [Google Scholar] [CrossRef] 
[9] Li, L., Li, C. and Li, H. (2018) An Analysis and Design for Time-Varying Structures Dynamical Networks via State Constraint Impulsive Control. International Journal of Control, 92, 2820-2828. [Google Scholar] [CrossRef] 
[10] Xie, R. and Li, C. (2019) Stability Analysis on Cohen-Grossberg Neural Networks with Saturated Impulse Inputs. Neural Processing Letters, 51, 1265-1283. [Google Scholar] [CrossRef] 
[11] 周金连, 刘琛, 刘东南. 基于脉冲控制的线性多智能体系统的二部一致性[J]. 佳木斯大学学报(自然科学版), 2021, 39(3): 164-167.
[12] 谢巧玲, 刘志鑫, 杨志春. 基于逻辑选择脉冲时滞动力系统的稳定性分析[J]. 重庆工商大学学报(自然科学版), 2023, 40(4): 63-68.
[13] Zhang, Y. (2017) Global Exponential Stability of Delay Difference Equations with Delayed Impulses. Mathematics and Computers in Simulation, 132, 183-194. [Google Scholar] [CrossRef] 
[14] Hu, T. and Lin, Z. (2001) Control Systems with Actuator Saturation: Analysis and Design. Birkhauser, 55-67.
[15] Lu, J., Ho, D.W.C. and Cao, J. (2010) A Unified Synchronization Criterion for Impulsive Dynamical Networks. Automatica, 46, 1215-1221. [Google Scholar] [CrossRef] 
[16] 刘豹, 谭万生. 现代控制理论[M]. 北京: 机械工业出版社, 2007.

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