基于T-S模糊模型的冠状动脉时滞系统同步研究
Synchronization Study for Coronary Artery Time-Delay Systems Based on T-S Fuzzy Model
摘要: 冠状动脉是给心脏供血的肌型血管，负责将氧气和营养物质输送到心脏血管，一旦血管阻塞和痉挛，会导致心血管以及血管痉挛等心脑血管疾病。为了治疗心脑血管疾病，了解冠状动脉血管痉挛的发病原理，实现冠状动脉系统的混沌同步是非常重要的。在实际工作中，冠状动脉系统的数学模型是难以精确构造的，而Takagi-Sugeno (T-S)模糊模型可以以任意精度逼近复杂的非线性系统，本文基于T-S模糊模型研究了冠状动脉系统的同步问题。本文考虑时滞对系统的影响，构造冠状动脉数学模型，结合Wirtinger积分不等式和一种新的二重积分不等式处理求导后的一重积分和二重积分，降低系统保守性，并基于并行分布式补偿方案，设计状态反馈控制器，有效实现了系统的同步。最后，通过仿真实例实现了本文方法的有效性。
Abstract: Coronary arteries are muscular blood vessels that supply blood to the heart and are responsible for transporting oxygen and nutrients to the heart vessels. Once the blood vessels are blocked and spasm, it will lead to cardiovascular and cerebrovascular diseases such as cardiovascular and vaso-spasm. In order to treat cardiovascular and cerebrovascular diseases, it is very important to understand the pathogenesis of coronary vasospasm and realize the chaotic synchronization of the coronary systems. In practice, the mathematical model of the coronary system is difficult to construct accurately, and the Takagi-Sugeno (T-S) fuzzy model can approximate complex nonlinear systems with arbitrary precision. This paper studies the synchronization of the coronary systems based on the T-S fuzzy model. This paper considers the effect of time-delay on the system, combines Wirt-inger integral inequality and a new double integral inequality to deal with the single integral and double integral after derivation, and reduces the conservatism of the system. Based on parallel distributed compensation scheme, the state feedback controller is designed, which effectively realizes the synchronization of the systems. Finally, the effectiveness of the method in this paper is realized through a simulation example.
文章引用：曹秋霞. 基于T-S模糊模型的冠状动脉时滞系统同步研究[J]. 计算机科学与应用, 2022, 12(2): 392-404. https://doi.org/10.12677/CSA.2022.122040

参考文献

[1] 朱涛, 张广军, 姚宏, 李睿. 滑模控制的时滞分数阶金融系统混沌同步[J]. 深圳大学学报(理工版), 2014, 31(6): 626-629.
[2] Tirandaz, H., Aminabadi, S.S. and Tavakoli, H. (2017) Chaos Synchronization and Parameter Identifica-tion of a Finance Chaotic System with Unknown Parameters, a Linear Feedback Controller. Alexandria Engineering Journal, 57, 1519-1524. [Google Scholar] [CrossRef] 
[3] Qi, W.H., Park, J.H., Cheng, J. and Kao, Y.G. (2017) Robust Stabilisation for Non-Linear Time-Delay Semi-Markovian Jump Systems via Sliding Mode Control. IET Control Theory & Applications, 11, 1504-1513. [Google Scholar] [CrossRef] 
[4] Wang, Y.W., Guan, Z.-H. and Wen, X.J. (2004) Adaptive Synchro-nization for Chen Chaotic System with Fully Unknown Parameters. Chaos Solitons & Fractals, 19, 899-903. [Google Scholar] [CrossRef] 
[5] Marouf, S., Esfanjani, R.M., Akbari, A., et al. (2016) T-S Fuzzy Controller Design for Stabilization of Nonlinear Networked Control Systems. Engineering Applications of Artifi-cial Intelligence, 50, 135-141. [Google Scholar] [CrossRef] 
[6] Long, S.H. and Zhong, S.M. (2017) H∞ Control for a Class of Singular Systems with State Time-Varying Delay. ISA Transactions, 66, 10-21. [Google Scholar] [CrossRef] [PubMed]
[7] Wang, J.A., Wen, X.-Y. and Hou, B.-Y. (2020) Advanced Stabil-ity Criteria for Static Neural Networks with Interval Time-Varying Delays via the Improved Jensen Inequality. Neuro-computing, 377, 49-56. [Google Scholar] [CrossRef] 
[8] Seuret, A. and Gouaisbaut, F. (2015) Hierarchy of LMI Condi-tions for the Stability Analysis of Time-Delay Systems. Systems & Control Letters, 81, 1-7. [Google Scholar] [CrossRef] 
[9] Tan, J.Y., Dian, S.Y., Zhao, T. and Chen, L. (2017) Stability and Stabilization of T-S Fuzzy Systems with Time Delay via Wirtinger-Based Double Integral Inequality. Neurocompu-ting, 275, 1063-1071. [Google Scholar] [CrossRef] 
[10] Park, M.J., Lee, S.H., Kwon, O.M. and Ryu, J.H. (2018) En-hanced Stability Criteria of Neural Networks with Time-Varying Delays via a Generalized Free-Weighting Matrix Inte-gral Inequality. Journal of the Franklin Institute, 355, 6531-6548. [Google Scholar] [CrossRef] 
[11] Lin, C.-J., Yang, S.-K. and Yau, H.T. (2012) Chaos Suppres-sion Control of a Coronary Artery System with Uncertainties by Using Variable Structure Control. Computers & Math-ematics with Applications, 64, 988-995. [Google Scholar] [CrossRef] 
[12] Seuret, A. and Gouaisbaut, F. (2013) Wirtinger-Based Integral Inequality: Application to Time-Delay Systems. Automatica, 49, 2860-2866. [Google Scholar] [CrossRef] 
[13] Zhao, N., Lin, C., et al. (2017) A New Double Integral Ine-quality and Application to Stability Test for Time-Delay Systems. Applied Mathematics Letters, 65, 26-31. [Google Scholar] [CrossRef] 
[14] Liu, K. and Seuret, A. (2017) Comparison of Bounding Methods for Stability Analysis of Systems with Time-Varying Delays. Journal of the Franklin Institute, 354, 2979-2993. [Google Scholar] [CrossRef]