具有leakage时滞的非线性系统的动态分析及控制

发布时间：2018-01-02 15:00

本文关键词：具有leakage时滞的非线性系统的动态分析及控制　出处：《江南大学》2016年博士论文　论文类型：学位论文

【摘要】：系统的历史状态会对当前的状态造成一定的影响,也就是说我们在考虑系统演化时不仅要顾及到当前的状态而且要考虑到过去的状态,甚至是过去状态的变化率.时滞也常常是系统振荡、不稳定的主要因素,因此对时滞的非线性系统进行分析与控制的研究具有重要的理论和实际价值.本文基于Lyapunov泛函方法、矩阵理论、不等式技巧、图论知识、随机微分方程等,主要考虑leakage时滞对几类神经网络和基因调控网络的动力学行为的影响.另一方面,近年来,数据采样控制技术和事件触发控制为系统控制理论提供了新思路.我们将这种方法用于具有leakage时滞的BAM和GRN的控制以及受到外界恶意输入影响的离散系统稳定性控制问题的研究.本文的研究工作具体如下:1.研究了具有采样数据反馈的leakage时滞的BAM神经网络指数稳定性问题,应用时间输入延迟的方法和不等式技巧,得到了确保系统指数稳定的充分条件.鉴于在实际应用中,获取的信号通常具有一定的持续性,为了研究这些滞后信号的累积效应,我们考虑了具有采样数据反馈的连续分布型leakage时滞的BAM神经网络稳定性问题.2.通过分析leakage时滞对BAM系统的影响,发现当系统无leakage时滞或时滞不超过一定范围时,系统是稳定的,而当leakage时滞超出某值时,系统变得不稳定.然后通过设计合适的采样控制器使得不稳定的系统趋于稳定,最后通过数值模拟来验证理论的有效性及可行性.类似的方法应用到基因调控网络上,依据Lyapunov泛函方法和线性矩阵不等式设计采样控制器使得不稳定的leakage时滞系统趋于稳定,并用数值实例表明理论的有效性.3.研究了涉及到leakage时滞,中立时滞等混合时滞的基因调控网络稳定性问题,推广和改进了一些文献的结论.应用随机微分方程等理论我们考虑了具有Markov切换和混合时间延迟的随机基因调控网路的稳定性,并且利用数值模拟验证理论的可行性.4.研究了受到攻击的线性离散系统的稳定性控制问题及其应用.首先讨论事件触发控制策略在受到依一定概率分布攻击的线性离散系统的稳定性问题中的应用,得到了使得系统均方最终有界的充分条件.并将这种方法应用到受攻击的多智能体系统中,得到了使得多智能体系统达到均方最终有界一致的充分条件,并用数值实例说明了理论的有效性。
[Abstract]:The history of the system state will cause a certain impact on the current state, that is to take into account not only the current state but also to take into account the past state we consider system evolution, and even change the past state rate. Time delay is often the system oscillation, the main cause of instability, so the analysis and Research on the time delay control of nonlinear systems has important theoretical and practical value. In this paper, the Lyapunov functional method, based on matrix theory and inequality technique, graph theory, stochastic differential equations, considering the dynamic behavior of main leakage regulation network delay on several kinds of neural networks and gene. On the other hand, in recent years, data sampling control the event triggered control technology and provides a new idea for system control theory. We apply this method to control with leakage BAM and GRN delay and to the outside world Study on the stability of the discrete system control effect of malicious input. The specific contents are as follows: 1. research on the BAM neural network with exponential stability of leakage time-delay feedback sampling data, method and inequality techniques, application time of input delay, the sufficient conditions to ensure the exponential stability of the system. In practical application, to obtain the signal usually has a certain degree of persistence, in order to study the cumulative effect of these delay signals, we consider a sampling of.2. BAM neural network stability problem of continuous distribution delay leakage data feedback through the analysis of the influence of delay on the leakage BAM system, found that when the leakage system without delay or delay does not exceed a certain range, the system is stable, while leakage delay beyond a certain value, the system becomes unstable. Then through the sampling control system makes the appropriate The instability of the system tends to be stable, finally through the numerical simulation to verify the validity and feasibility of the theory. A similar method is applied to the gene regulatory network, according to the Lyapunov functional method and linear matrix inequality design sampling controller makes leakage time-delay system instability tends to be stable, and the numerical examples show that the effectiveness of.3. theory research involving to leakage delay, the stability of gene regulatory network of neutral delay mixed delays, improve and generalize some results in the literature. The application of stochastic differential equation theory, we consider the stability of stochastic gene regulatory network of Markov switching and mixing time delay, the stability control problem and its application feasibility of.4. and numerical simulation verify the theoretical research linear discrete systems under attack. First discuss the event triggered control strategy are in accordance with The application of stability of the linear discrete system with a certain probability distribution in the attack, we obtain sufficient conditions for the system are ultimately bounded. And this method is applied to multi-agent systems under attack, for the multi-agent system reached final some sufficient conditions for boundedness and uniform, and the the validity of the theory with a numerical example.

【学位授予单位】：江南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP13

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