具有未知转移概率Markovian神经网络渐近稳定性研究

doi:10.16182/j.issn1004731x.joss.201702001

系统仿真学报 ›› 2017, Vol. 29 ›› Issue (2): 235-240.doi: 10.16182/j.issn1004731x.joss.201702001

• 仿真建模理论与方法 • 下一篇

具有未知转移概率Markovian神经网络渐近稳定性研究

路阳¹, 衣淑娟¹, 任伟建², 刘建东³

1.黑龙江八一农垦大学信息技术学院,黑龙江大庆 163319;
2.东北石油大学电气信息工程学院,黑龙江大庆 163318;
3.北京电子工程总体研究所北京 100854

收稿日期:2015-05-06 修回日期:2015-07-21 出版日期:2017-02-08 发布日期:2020-06-01
作者简介:路阳(1976-),男,黑龙江双城,博士,副教授,研究方向为非线性随机系统故障检测。
基金资助:
国家自然科学基金(61374127,61422301),黑龙江省杰出青年科学基金(JC2015016),黑龙江自然科学基金(F201428),黑龙江省农垦总局重点科技计划项目(HNK125B-04-03)

Research on Asymptotic Stability for Markovian Jumping Neural Network with Unknown Transition Probabilities

Lu Yang¹, Yi Shujuan¹, Ren Weijian², Liu Jiandong³

1. College of Information and Technology, Heilongjiang Bayi Agricultural University, Daqing 163319, China;
2. College of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China;
3. Beijing Institute of Electronic System Engineering, Beijing 100854, China

Received:2015-05-06 Revised:2015-07-21 Online:2017-02-08 Published:2020-06-01

摘要/Abstract

摘要： 针对一类具有部分未知转移概率的离散时延Markovian跳跃神经网络系统,建立了更具一般代表性的随机神经网络动力学模型,研究其渐近稳定性问题。假定转移概率部分元素未知,系统中的不确定为范数有界,基于Lyapunov稳定性理论,通过构造适合的Lyapunov-Krasovskii泛函并利用随机分析方法,给出了离散Markovian神经网络系统全局渐近稳定的充分性判据。通过Matlab的LMI工具箱,求解线性矩阵不等式对判据进行检验,新的判据减少了结果的保守性。数值仿真算例验证了所给判据的有效性。

关键词: 神经网络, 马尔可夫跳跃参数, 部分未知转移概率, 渐近稳定性

Abstract: The analysis problem of asymptotic stability for a class of uncertain neural networks with Markovian jumping parameters and time delays was addressed. The general representative dynamic stochastic neural network model was established. The considered transition probabilities were assumed to be partially unknown. The parameter uncertainties were considered to be norm-bounded. Based on Lyapunov stability theory, by constructing a suitable Lyapunov-Krasovskii function and using the stochastic analysis method, some sufficient criteria for the stability of discrete Markovian neural networks was derived. Through the Matlab LMI toolbox, solving a set of linear matrix inequalities to test criterion, the new criterion reduced the conservatism of the results. A numerical example illustrates the effectiveness of the proposed theory.

Key words: neural networks, Markovian jumping parameters, partly unknown transition probabilities, asymptotic stability

中图分类号:

TP391.9

路阳, 衣淑娟, 任伟建, 刘建东. 具有未知转移概率Markovian神经网络渐近稳定性研究[J]. 系统仿真学报, 2017, 29(2): 235-240.

Lu Yang, Yi Shujuan, Ren Weijian, Liu Jiandong. Research on Asymptotic Stability for Markovian Jumping Neural Network with Unknown Transition Probabilities[J]. Journal of System Simulation, 2017, 29(2): 235-240.

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具有未知转移概率Markovian神经网络渐近稳定性研究

Research on Asymptotic Stability for Markovian Jumping Neural Network with Unknown Transition Probabilities

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