广东工业大学学报 ›› 2017, Vol. 34 ›› Issue (01): 78-83,89.doi: 10.12052/gdutxb.150151

• 综合研究 • 上一篇    下一篇

不确定时滞神经网络的无源性分析

彭诗友, 彭世国   

  1. 广东工业大学 自动化学院, 广东 广州 510006
  • 收稿日期:2015-12-28 出版日期:2017-01-09 发布日期:2017-01-09
  • 作者简介:彭诗友(1989-),男,硕士研究生,主要研究方向为神经网络无源性分析.
  • 基金资助:

    国家自然科学基金资助项目（61374081）；广东省自然科学基金资助项目（S2013010013034，2015A030313485）

Passivity Analysis for Uncertain Neural Networks with Time-Varying Delay

Peng Shi-you, Peng Shi-guo   

  1. School of Automation, Guangdong University of Technology, Guangzhou 510006, China
  • Received:2015-12-28 Online:2017-01-09 Published:2017-01-09

HTML

PDF (PC)

2901

摘要：

对神经网络系统的无源性进行了研究，根据无源性网络理论，得出神经网络满足无源保守性更弱的条件.另外研究了参数不确定时滞神经网络的鲁棒无源性.根据李雅普诺夫稳定性理论、Jensen不等式、Schur补及自由权矩阵等方法，研究表明，从构造一个新颖李雅普诺夫泛函并化简李雅普诺夫泛函导数的二次积分项，能够得到神经网络保守性更小的无源条件.同时，得到了满足神经网络无源条件的李雅普诺夫泛函的所有二次项对称矩阵可非正定.实验仿真证明了本文方法的有效性.

关键词: 神经网络, 李雅普诺夫泛函, 时滞, 无源

Abstract:

The passivity of neural networks of neural network systems is studied. Based on the passive network theory, it the less conservative conditions of the neural network can be obtained. Additionally, the robust passivity of the parameters uncertainties' neural networks with time-delay is analyzed. According to theories and approaches of Lyapunov stability, Jensen integral inequality, Schur complement lemma and free weighting matrices, the research shows that the less conservative passive condition of the neural network can be obtained from constructing a new Lyapunov-Krasovskii functional and simplifying the quadratic terms of the Lyapunov-Krasovskii functional's inverse. Meanwhile, the passivity condition is obtained not requiring all the symmetric involved in the employed quadratic Lyapunov-Krasovskii functional matrices to be positive definite. The results show that the method is effective.

Key words: neural networks, Lyapunov-Krasovskii functional, time delay

中图分类号: 

  • TP273

[1] GUPTA M, JIN L, Homma N. Static and Dynamic Neural Networks:From Fundamentals to Advanced Theory[M]. New York:Wiley-IEEE Press, 2003.
[2] 郑胜林, 彭明明, 潘保昌. 一种基于Hough变换的神经网络字符识别方法[J]. 广东工业大学学报, 2003, 20(4):73-77. ZHENG S L, PENG M M, PAN B C. A method for characters recognition based on the hough transform and neural network[J]. Journal of Guangdong University of Technology, 2003, 20(4):73-77.
[3] ENSARI T, ARIK S. Global stability of a class of neural networks with time-varying delay[J]. IEEE Transactions on Circuits Systems II:Analog and Digital Signal Processing, 2005, 52(2):126-130.
[4] KWON O M, PARK J H, Lee S M. On robust stability for uncertain cellular neural networks with interval time varying delays[J]. IET Control Theory & Applications, 2008, 2(7):625-634.
[5] KWON O M, PARK J H. Delay dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays[J]. Journal of the Franklin Institute, 2008, 345(7):766-778.
[6] ZHU Q X, CAO J D. Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays[J]. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(3):467-479.
[7] ZHANG C K, HE Y, LI J, et al. Delay-dependent stability criteria for generalized neural networks with two delay components[J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(7):1263-1276.
[8] HILL D, MOYLAN P. The stability of nonlinear dissipative systems[J]. IEEE Transactions on Automatic Control, 1976, 21(5):708-711.
[9] LOZANO R, BROGLIATO B, EGELAND O, et al. Dissipative Systems Analysis and Control:Theory and Applications[M]. London, UK.:Springer, 2007.
[10] XIE L H, FU M Y, LI H Z. Passivity analysis and passification for uncertain signal processing systems[J]. IEEE Transactions on Signal Process, 1998, 46(9):2394-2403.
[11] WU C W. Synchronization in arrays of coupled nonlinear systems:passivity circle criterion and observer design[J]. IEEE Transactions on Circuits and Systems. I:Fundamental Theory and Applications, 2001, 48(10):1257-1261.
[12] LI C G, LIAO X F. Passivity analysis of neural networks with time delay[J]. IEEE Transactions on Circuits and Systems II:Analog and Digital Signal Processing, 2005, 52(8):471-475.
[13] LOU X Y, CUI B T. Passivity analysis of integro-differential neural networks with time-varying delays[J]. Neurocomputing, 2007, 70(4-6):1071-1078.
[14] ZHU J, LENG Q K, ZHANG Q L. Delay-dependent passivity criterion for hopfield neural networks[C]. 2010 Chinese Control and Decision Conference, Xuzhou, China, 2010:1267-1272.
[15] ZENG H B, HE Y, WU M, et al. Passivity analysis for neural with a time-varying delay[J]. Neurocomputing, 2011, 74(5):730-734.
[16] ZENG H B, XIAO S P, ZHANG C F, et al. Further results on passivity analysis of neural networks with time-varying delay[C], 26th Chinese Control and Decision Conference (CCDC), Changsha, China, 2014:161-165.
[17] ZHANG B Y, XU S Y, LAM J. Relaxed passivity condition for neural networks with time-varying delays[J]. Neurocomputing, 2014, 142(1):299-306.
[18] WANG Z D, LIU Y R, LIU X H. Global exponential stability of generalized recurrent neural networks with discrete and distributed delays[J]. Neural Networks, 2006, 19(5):667-675.
[19] GU K. An integral inequality in the stability problem of time-delay systems[C]. Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, 3(3):2805-2810.
[20] PARK P G, KO J W, JEONG C. Reciprocally convex approach to stability of systems with time-varying delays[J]. Automatica, 2011, 47(1):235-238.
[21] BOYD S, GHAOHUI L E, FERON E, et al. Linear matrix inequalities in system and control theory[M]. Philadelp-hiaz:SIAM, 1994.
[22] PETERSEN I R, HOLLOT C V. A Riccati equation approach to the stabilization of uncertain linear systems[J]. Automatica, 1986, 22(4):397-411.
[1] 谢国波, 林立, 林志毅, 贺笛轩, 文刚. 基于YOLOv4-MP的绝缘子爆裂缺陷检测方法[J]. 广东工业大学学报, 2023, 40(02): 15-21.
[2] 张锐, 吕俊. 基于分离结果信噪比估计与自适应调频网络的单通道语音分离技术[J]. 广东工业大学学报, 2023, 40(02): 45-54.
[3] 邱俊豪, 程志键, 林国怀, 任鸿儒, 鲁仁全. 具有执行器故障的非线性系统指定性能控制[J]. 广东工业大学学报, 2023, 40(02): 55-63.
[4] 陈靖宇, 吕毅. 基于脉冲神经网络的冷链制冷机结霜检测方法[J]. 广东工业大学学报, 2023, 40(01): 29-38.
[5] 叶文权, 李斯, 凌捷. 基于多级残差U-Net的稀疏SPECT图像重建[J]. 广东工业大学学报, 2023, 40(01): 61-67.
[6] 彭美春, 阳晨, 李君平, 叶伟斌, 黄文伟. 基于BP神经网络的车辆碳排放测算研究[J]. 广东工业大学学报, 2023, 40(01): 107-112.
[7] 刘洪伟, 林伟振, 温展明, 陈燕君, 易闽琦. 基于MABM的消费者情感倾向识别模型——以电影评论为例[J]. 广东工业大学学报, 2022, 39(06): 1-9.
[8] 章云, 王晓东. 基于受限样本的深度学习综述与思考[J]. 广东工业大学学报, 2022, 39(05): 1-8.
[9] 彭积广, 肖涵臻. 模型预测控制下多移动机器人的跟踪与避障[J]. 广东工业大学学报, 2022, 39(05): 93-101.
[10] 黎耀东, 任志刚, 吴宗泽. 基于深度神经网络的注塑过程预测控制[J]. 广东工业大学学报, 2022, 39(05): 120-126,136.
[11] 曾江毅, 李志生, 欧耀春, 金宇凯. 季节指数改进的PM2.5质量浓度组合预测模型研究[J]. 广东工业大学学报, 2022, 39(03): 89-94.
[12] Gary Yen, 栗波, 谢胜利. 地球流体动力学模型恢复的长短期记忆网络渐进优化方法[J]. 广东工业大学学报, 2021, 38(06): 1-8.
[13] 郭心德, 丁宏强. 离散制造智能工厂场景的AGV路径规划方法[J]. 广东工业大学学报, 2021, 38(06): 70-76.
[14] 黄剑航, 王振友. 基于特征融合的深度学习目标检测算法研究[J]. 广东工业大学学报, 2021, 38(04): 52-58.
[15] 马少鹏, 梁路, 滕少华. 一种轻量级的高光谱遥感图像分类方法[J]. 广东工业大学学报, 2021, 38(03): 29-35.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2017 《广东工业大学学报》编辑部
地址：广州市东风东路729号广东工业大学 邮编：510090
电话：020-37626653,020-37626139,020-37626396
邮箱：xbzrb@gdut.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发