具有饱和脉冲输入神经网络的局部指数同步

doi:10.12341/jssms21186

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (3): 542-554.DOI: 10.12341/jssms21186

具有饱和脉冲输入神经网络的局部指数同步

何志龙^1,2, 陈小昆¹

1. 新疆财经大学统计与数据科学学院, 乌鲁木齐 830012;
2. 西南大学电子信息工程学院, 重庆 400715

收稿日期:2021-04-19 修回日期:2021-09-07 出版日期:2022-04-20 发布日期:2022-04-20
通讯作者: 吴艳霞,Email:xindahzl@126.com.
基金资助:
国家重点研发计划（2018AAA0100101），国家自然科学基金（61633011，61873213），新疆维吾尔自治区自然科学基金青年基金（2022D01B13），新疆财经大学校级科研项目-高层次人才专项（2022XGC065）资助课题.

PDF ( 167 ) 引用

何志龙, 陈小昆. 具有饱和脉冲输入神经网络的局部指数同步[J]. 系统科学与数学, 2022, 42(3): 542-554.

HE Zhilong, CHEN Xiaokun. Local Exponential Synchronization of Neural Network with Saturated Impulsive Inputs[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(3): 542-554.

Local Exponential Synchronization of Neural Network with Saturated Impulsive Inputs

HE Zhilong^1,2, CHEN Xiaokun¹

1. School of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi 830012;
2. College of Electronic and Information Engineering, Southwest University, Chongqing 400715

Received:2021-04-19 Revised:2021-09-07 Online:2022-04-20 Published:2022-04-20

文章通过设计一类具有执行器饱和的脉冲控制器来获得驱动响应神经网络的混沌同步.首先分别利用扇区非线性模型法和多面体表示法处理了脉冲时刻的系统的饱和非线性.其次，通过选取适当的二次Lyapunov函数，结合数学归纳法获得了线性矩阵不等式（LMIs）相关的局部指数同步准则.最后，通过一个数值例子验证了结论的有效性.

关键词： 神经网络, 脉冲控制, 执行器饱和, 局部指数同步, 初值可容许集

In this paper, we design a kind of impulsive controller with actuator saturation to obtain chaotic synchronization of the drive-response neural network. Firstly, we use the sector nonlinear model method and the polyhedral representation method to deal with the saturation nonlinearity of the system at the impulse moment. Secondly, by selecting the appropriate quadratic Lyapunov function, combined with mathematical induction to obtain the local exponential synchronization criterion related to linear matrix inequalities (LMIs). Finally, a numerical example is used to verify the validity of the conclusion.

Key words: Neural network, impulsive control, actuator saturation, local exponential synchronization, initial admissible set

MR(2010)主题分类:

分享此文:

[1] Hopfield J J. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States of America, 1982, 79:2554-2558.
[2] Chua L O, Yang L. Cellular neural networks:Applications. IEEE Transactions on Circuits and Systems, 1988, 35(10):1273-1290.
[3] Cohen M A. Grossberg S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man, and Cybernetics SMC, 1983, 13(5):815-826.
[4] He Z L, Li C D, Chen L, et al. Dynamic behaviors of the FitzHugh-Nagumo neuron model with state-dependent impulsive effects. Neural Networks, 2020, 121:497-511.
[5] He Z L, Li C D, Li H F, et al. Global exponential stability of high-order Hopfield neural networks with state-dependent impulses. Physica A:Statistical Mechanics and Its Applications, 2020, 542:123434-1-21.
[6] Zhang H G, Yang F S, Liu X D, et al. Stability analysis for neural networks with time-varying delay based on quadratic convex combination. IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(4):513-521.
[7] He Z L, Li C D, Cao Z R, et al. Periodicity and global exponential periodic synchronization of delayed neural networks with discontinuous activations and impulsive perturbations. Neurocomputing, 2021, 431:111-127.
[8] Pecora L M, Carroll T L. Synchronization in chaotic systems. Physical Review Letters, 1990, 64(8):821-824.
[9] Lu H. Chaotic attractors in delayed neural networks. Physics Letters A, 2002, 298(2):109-116.
[10] Li C D, Liao X F, Wong K W. Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication. Physica D:Nonlinear Phenomena, 2004, 194(3-4):187-202.
[11] Zou F, Nossek J A. A chaotic attractor with cellular neural networks. IEEE Transactions on Circuits and Systems, 1991, 38(7):811-812.
[12] Chen G R, Zhou J, Liu Z R. Global synchronization of coupled delayed neural networks and applications to chaotic CNN models. International Journal of Bifurcation and Chaos, 2004, 14(7):2229-2240.
[13] Yang T, Chua L O. Impulsive stabilization for control and synchronization of chaotic systems:Theory and application to secure communication. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications, 1997, 44(10):976-988.
[14] Heagy J F, Carroll T L, Pecora L M. Experimental and numerical evidence for riddled basins in coupled chaotic systems. Physical Review Letters, 1994, 73(26):3528.
[15] Cao J D, Li H, Ho D W. Synchronization criteria of Lur'e systems with time-delay feedback control. Chaos Solitons & Fractals, 2005, 23(4):1285-1298.
[16] Huang D B. Simple adaptive-feedback controller for identical chaos synchronization. Physical Review E, 2005, 71(3):037203.
[17] Yang Y Q, Cao J D. Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects. Physica A:Statistical Mechanics and Its Applications, 2007, 386(1):492-502.
[18] Li X D, Fu X L. Lag synchronization of chaotic delayed neural networks via impulsive control. IMA Journal of Mathematical Control and Information, 2012, 29(1):133-145.
[19] Li X D, Rakkiyappan R. Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(6):1515-1523.
[20] He Z L, Li C D, Cao Z R, et al. Stability of nonlinear variable-time impulsive differential systems with delayed impulses. Nonlinear Analysis:Hybrid Systems, 2021, 39:100970.
[21] Lu J G, Chen G R. Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control:An LMI approach. Chaos Solitons & Fractals, 2009, 41(5):2293-2300.
[22] Li P, Cao J D, Wang Z D. Robust impulsive synchronization of coupled delayed neural networks with uncertainties. Physica A:Statistical Mechanics and Its Applications, 2007, 373:261-272.
[23] Zhang Y P, Sun J T. Robust synchronization of coupled delayed neural networks under general impulsive control. Chaos Solitons & Fractals, 2009, 41(3):1476-1480.
[24] Guan K Z. Global power-rate synchronization of chaotic neural networks with proportional delay via impulsive control. Neurocomputing, 2018, 283(29):256-265.
[25] Xu Z L, Peng D X, Li X D. Synchronization of chaotic neural networks with time delay via distributed delayed impulsive control. Neural Networks, 2019, 118:332-337.
[26] Hu T S, Lin Z L. Control Systems with Actuator Saturation:Analysis and Design. Boston, MA:Birkhäuser:Springer Science & Business Media, 2001.
[27] Tarbouriech S, Garcia G, da Silva J M G, et al. Stability and Stabilization of Linear Systems With Saturating Actuators. London, U.K.:Springer, 2011.
[28] Wu Z G, Shi P, Su H Y, et al. Local synchronization of chaotic neural networks with sampled-data and saturating actuators. IEEE Transactions on Cybernetics, 2014, 44(12):2635-2645.
[29] Li H F, Li C D, Ouyang D Q, et al. Impulsive synchronization of unbounded delayed inertial neural networks with actuator saturation and sampled-data control and its application to image encryption. IEEE Transactions on Neural Networks and Learning Systems, 2021, 32(4):1460-1473.
[30] He Z L, Li C D, Cao Z R, et al. Exponential stability of discrete-time delayed neural networks with saturated impulsive control, IET Control Theory and Applications, 2021, 15(12):1628-1645.
[31] Wang H O, Tanaka K, Griffin M F. An approach to fuzzy control of nonlinear systems:stability and design issues. IEEE Transactions on Fuzzy Systems, 1996, 4(1):14-23.

[1]	胡雪梅, 李佳丽, 蒋慧凤. 机器学习方法研究肝癌预测问题[J]. 系统科学与数学, 2022, 42(2): 417-433.
[2]	王秋雨, 张举勇. 一种基于三维对齐方式的深度学习人脸识别算法[J]. 系统科学与数学, 2021, 41(7): 2035-2045.
[3]	吴峰, 于洋. PMSM伺服系统的神经网络动态面控制[J]. 系统科学与数学, 2021, 41(5): 1203-1214.
[4]	胡雪梅, 蒋慧凤. 具有技术指标的逻辑回归模型预测谷歌股票的涨跌趋势[J]. 系统科学与数学, 2021, 41(3): 802-823.
[5]	姚海祥, 黎俊伟, 夏晟皓, 陈树敏. 基于Apriori算法和神经网络的模糊交易决策[J]. 系统科学与数学, 2021, 41(10): 2868-2891.
[6]	陆文星，戴一茹，李楚，李克卿. 基于改进PSO-BP神经网络的旅游客流量预测方法[J]. 系统科学与数学, 2020, 40(8): 1407-1419.
[7]	齐雪，才治军. 船用锅炉主蒸汽压力系统的多工况控制[J]. 系统科学与数学, 2019, 39(6): 831-844.
[8]	贾凯，倪志伟，李敬明，陆玉佳，朱旭辉. 基于改进二进制人工蜂群的BP神经网络并行集成学习算法及其应用研究[J]. 系统科学与数学, 2019, 39(3): 477-494.
[9]	王溪，明扬，洪奕光. 基于群论的深度卷积网络分析[J]. 系统科学与数学, 2019, 39(2): 219-227.
[10]	李祥坤，杨争峰，曾霞，刘志明. 一种面向图像识别的神经网络通用扰动生成算法[J]. 系统科学与数学, 2019, 39(12): 1944-1963.
[11]	相鑫，刘秀丽. 四层参数自调整BP神经网络模型及其在人口死亡率预测中的应用[J]. 系统科学与数学, 2018, 38(6): 702-710.
[12]	王乐，何舒平. 基于Kleinman迭代算法的非线性系统自适应控制器设计[J]. 系统科学与数学, 2017, 37(9): 1885-1892.
[13]	罗世贤，陈武华. 一类随机反应扩散神经网络的周期间歇采样控制[J]. 系统科学与数学, 2017, 37(3): 652-664.
[14]	任水利，雷蕾，甘旭升，吴亚荣. 基于粗糙集与小波网络集成的股票价格走势预测研究[J]. 系统科学与数学, 2017, 37(11): 2208-2221.
[15]	胡凯，曾喆昭. 一种新型自抗扰控制自适应非线性控制律[J]. 系统科学与数学, 2016, 36(12): 2179-2186.

阅读次数

全文

摘要