几类微分动力系统的非固定时刻脉冲控制

发布时间：2018-03-06 19:17

本文选题：Luré系统　切入点：脉冲时窗　出处：《重庆师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：在给系统设置脉冲时,我们并不能确保正好在固定时刻上施加脉冲,即我们原本打算在t时刻设置脉冲,却只能在一个很小的时间窗口(t-a,t+a)上讨论问题,其中a是一个很小的正数。在系统中,不稳定脉冲和稳定脉冲同时存在,是时变脉冲的一个重要特征,一般情况,有两种脉冲动力系统,分别是不稳定的脉冲序列和稳定的脉冲序列,其中前者是指能抑制动力系统的稳定性,后者是指能增强动力系统的稳定性。本文对不确定Luré系统进行了时间窗口分析、对非自治混沌系统进行了时间窗口分析、对时滞耦合神经网络进行了时变脉冲分析。针对系统设置脉冲时间窗口问题,可以利用构造Lyapunov函数、不等式技巧、比较定理和数学归纳法来证明其稳定性,只是已经不在固定点设置脉冲,而是在一个很小的时间窗口施加,最后得出自己的结论。针对时滞耦合神经系统施加时变脉冲问题,利用构造Lyapunov函数法,再应用全局指数稳定的定义来证明稳定性,最后得到时变脉冲时滞耦合神经网络的稳定性。本文的结构如下:第一章对Luré系统进行了脉冲时窗下的稳定性分析,应用比较系统得到了脉冲控制系统稳定所满足的条件,最后通过数值模拟说明了定理的成立。第二章对非自治混沌系统进行了脉冲时窗下的稳定性与同步性分析,利用数学归纳法来证明其稳定性,最后数值模拟说明定理成立。第三章对时滞耦合神经网络进行时变脉冲下的稳定性分析,我们把不稳定脉冲和稳定脉冲都考虑进去了,通过控制时变脉冲强度,利用指数稳定的定义得到时变脉冲时滞耦合神经网络是指数稳定的,最后通过数值模拟表明了理论结果的有效性。
[Abstract]:When we set a pulse to the system, we can't be sure to apply it exactly at a fixed time, that is, we were going to set the pulse at t time, but we could only discuss the problem at a very small time window. Where a is a very small positive number. In the system, unstable pulses and stable pulses exist simultaneously, which is an important characteristic of time-varying pulses. In general, there are two kinds of impulsive dynamical systems. They are unstable impulses and stable impulses, in which the former refers to the stability of the dynamic system, the latter is to enhance the stability of the dynamic system. In this paper, the time-window analysis of the uncertain Lur 茅 system is carried out. Time window analysis of nonautonomous chaotic systems and time-varying impulsive analysis of time-delay coupled neural networks are carried out. For the problem of setting impulsive time windows for the system, Lyapunov functions can be constructed and inequality techniques can be used. The comparison theorem and mathematical induction are used to prove its stability, but the pulse is not set at the fixed point, but is applied in a very small time window. Finally, we draw our own conclusion, and apply the time-varying pulse to the time-delay coupled nervous system. Using the method of constructing Lyapunov function and applying the definition of global exponential stability, the stability is proved. Finally, the stability of time-varying impulsive time-delay coupled neural networks is obtained. The structure of this paper is as follows: in Chapter 1, the stability of Lur 茅 system under impulsive time-window is analyzed, and the stability conditions of impulsive control system are obtained by comparing the system. In the second chapter, the stability and synchronism of nonautonomous chaotic systems under impulsive time-windows are analyzed, and its stability is proved by mathematical induction. Finally, numerical simulation shows that the theorem holds. In chapter 3, we analyze the stability of time-varying impulses in coupled neural networks with time-delay. We take both unstable and stable pulses into account, and control the intensity of time-varying pulses. By using the definition of exponential stability, it is found that the time-varying impulsive time-delay coupled neural networks are exponentially stable. Finally, numerical simulation shows the validity of the theoretical results.
【学位授予单位】：重庆师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175

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