随机时滞神经网络输入状态稳定性研究

发布时间：2018-01-01 00:33

本文关键词：随机时滞神经网络输入状态稳定性研究　出处：《广东工业大学》2016年硕士论文　论文类型：学位论文

【摘要】：近年来,随着随机神经网络在组织优化、信号处理、模式识别以及人工智能领域的广泛应用,随机神经网络稳定性越来越受到更多人的关注。就目前来说,随机神经网络的稳定性已经有了许多成果。但是在实际中,控制系统经常会受到干扰,例如控制中的一些微小变动,以及观察中存在的误差。因此要求控制系统不仅要稳定,还需要求控制系统输入状态稳定(ISS)。本文在李雅普诺夫泛函、伊藤公式和随机微分方程的基础上,研究了随机Hopfield神经网络三类时滞模型的输入状态稳定性。本文的主要内容如下：首先,概括描述了本课题的研究背景、研究现状和意义,并给出了研究中存在的基本问题。之后,介绍了Jensen不等式、伊藤公式、Schur补引理、线性矩阵不等式(LMI)、Lyapunov稳定性理论、输入状态稳定性定义、SISS-Lyapunov-Krasovaskii稳定性定理以及一些常用的引理。其次,对本文所研究的问题进行了相应的问题描述,然后分别给出随机时滞Hopfield神经网络模型,并就变时滞、多变时滞和区间时滞等三类时滞模型进行了随机输入稳定性分析。通过构造合适的SISS-Lyapunov-Krasovaskii泛函,利用伊藤公式处理随机微分方程模型。使用Jensen不等式、Schur补引理以及其他几个重要的不等式对求导结果进行分析,在分析中将泛函的求导结果进行适当放缩,从而得到系统输入状态稳定的条件,并将带时滞的随机神经网路的随机输入稳定的充分条件通过LMI的形式给出,从而把随机神经网络的输入状态稳定性的问题转化为线性矩阵不等式可行性的问题。之后,给出算例验证可行性。最后,对全文进行总结与展望,指出本文的研究成果以及下一步研究的方向。本文所采取的SISS-Lyapunov-Krasovaskii泛函结合了基础的状态变量二次项和交叉积分项,在分析系统的随机输入状态稳定性问题时,全面考虑到系统的随机项以及存在各类变时滞,减少了所得结果的保守性。最后得出的结果比较容易采用MATLAB的LMI工具箱去验证结果可行性。后面的图形仿真也表明,本文所得到的随机输入状态稳定的充分条件的有效性。
[Abstract]:In recent years, with the wide application of stochastic neural networks in the fields of tissue optimization, signal processing, pattern recognition and artificial intelligence, the stability of stochastic neural networks has attracted more and more attention. Many achievements have been made in the stability of stochastic neural networks, but in practice, the control systems are often disturbed, such as some minor changes in control. Therefore, the control system should not only be stable, but also need to obtain the stability of the input state of the control system. In this paper, the Lyapunov Functionals are presented. On the basis of Ito formula and stochastic differential equation, the input state stability of three delay models of stochastic Hopfield neural network is studied. The main contents of this paper are as follows: first. This paper briefly describes the research background, research status and significance, and gives the basic problems in the research. Then, the Jensen inequality and the Ito formula Schur complementary Lemma are introduced. Linear matrix inequalities (LMI) and Lyapunov stability theory, the definition of input state stability. SISS-Lyapunov-Krasovaskii stability theorem and some common Lemma. Secondly, the problems studied in this paper are described. Then the stochastic delay Hopfield neural network model is given, and the time delay is changed. The stochastic input stability analysis of three kinds of time-delay models, such as variable delay and interval delay, is carried out. Appropriate SISS-Lyapunov-Krasovaskii Functionals are constructed. The stochastic differential equation model is treated by Ito formula. The derivation results are analyzed by using Jensen inequality and several other important inequalities. In the analysis, the derivation results of the functional are properly scaled to obtain the condition of the stability of the input state of the system, and the sufficient condition for the stochastic input stability of the stochastic neural network with time delay is given by LMI. So the stability of the input state of the stochastic neural network is transformed into the feasibility of linear matrix inequality (LMI). After that, an example is given to verify the feasibility. Finally, the full text is summarized and prospected. The SISS-Lyapunov-Krasovaskii functional adopted in this paper combines the quadratic terms of basic state variables and the cross product. Itemized. In analyzing the stability of the stochastic input state, the stochastic term of the system and the existence of all kinds of time-varying delays are taken into account. The result is easy to use MATLAB LMI toolbox to verify the feasibility of the result. In this paper, the sufficient conditions for the stability of random input states are obtained.
【学位授予单位】：广东工业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175

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