【作者】 马军；

【导师】 唐国宁；

【作者基本信息】 广西师范大学 ， 理论物理， 2003， 硕士

【摘要】 近二十年来，混沌的控制与同步研究引起了人们极大的兴趣，取得了丰富的成果，本文对此作了简要的综述。首先介绍了混沌的特征和刻画其特征的主要手段，然后介绍了一些混沌控制和同步的方法，在此基础上，本文提出了一些方法用于四维L.C振子超混沌系统的控制和同步，取得了比较好的结果。 四维L.C振子电路系统结构简单，具有复杂的动力学行为，是一个超混沌系统，对该系统进行同步与控制的研究将具有潜在价值。本文针对这个模型做了以下工作。 （1） 考虑到信号在传输过程中会发生失真，通常把公共信道对信号的影响用一个增益数K_c（t）来表示，将混沌信号x_i和一个标准直流信号S（t）经过公共信道同时发送，经过公用时变信道后信号失真为K_c（t）x_i（t）和K_c（t）S（t），在接收系统的前端设计了一个自适应信号补偿器来恢复信号，补偿器的增益K_r，在文献[115-116]基础上，本文经理论分析得到新的K_r表达式如下： Kr=δ／ln p=δ／KcS 其中δ的值有下列方程确定： δ=-a（K_cS）（K_rK_cS-s）ln p=-a（K_cS）²（δ-S） 模拟结果表明：采用本文提出的补偿增益K_r，可以很快的将信号恢复。 （2） 采用文献[117-118]提出的参数辨识方法，通过选取更一般的增益函数： l_i（x_i）=kx_i i=1,2,3 并根据系统输出变量的时间序列给出参数观测器的初始值来进行参数辨识，数值模拟结果表明：采用本文的参数观测器，在系统参数固定或变化的情况下，都可对系统未知参数实现快速高精度辨识，辨识的速度快于文献[117-118]提出的方法；在辨识参数的同时，结合参数补偿器，使两个参数不匹配的超混沌系统同步。 （3） 基于稳定性理论，通过构造Lyapunov函数， V（t）=（x₂（t）-y₂（t））²+（x₂（t）-y₂（t）+（?）₂（t）-（?）₂（t））²=e₂²+（e₂+（?）₂）² 得到控制器u₁=（2-b+a）e₁+（1-b）²e₂-e₃，采用类似理论分析方法，得到参数不匹配下同步所需要的控制器表达式。理论分析和数值计算表明：采用本文的控制器可使两个超混沌 系统同步。 （4）根据文献［82，104］的结果，采用间歇驱动或滤波反馈可以使两个参数匹配的混淹系 统达到同步，本文选取如下形式的控制器 G。二 （k：；一 k；y；）P（t）＝ k：（；x；）P（t）十 （：k。）y；p中)i＝ l，2，3 p（t）＝l，nTstsnT＋r、p（t）＝0，nT＋rstsnT＋T 对L．C振子超混炖系统进行同步研究，数值结果：采用这种控制器可使两个超混饨系统在参 数匹配和不匹配下都可以达到同步。 （5）采用 APD方法，选取新的驱动信号 S＝X1一ex来同步响应系统，理论分析和数值结果表 明：采用本文的驱动信号可以使两个超混饨系统同步，和文献【1141相比，采用本文的驱 动信号可使同步暂态过程更短。 历)利用外部标准参考信号个和／O来控制＊＊振子超混炖系统，基于稳定性理论，通过 构造L)apunov函数， Kgb （xz4L4）‘＋N)－L小t4－xzc KO＝k0卜ro’十个N－xsN＋／N一大0‘ 得到控制器表达式如下： u；＝Zr＋Zr＋。－（1－b）’x。一归一b＋。“＋x。 11、＝aH＋W十厂I十＊二aS一ie】JU一Q上一0卜那不一K十冽1一o厂o一Ue0／十z／十二I) ＋PP。＊2a＋a“／P＊lh、cpc／dx4＋d（x．）H(x41 理论分析和数值计算表明，采用这种控制器可以将系统控制到固定点和周期轨道上， 基于稳定性分析，选取控制器 D一a十八。了。x。三1 U，＝K，X，十K－K，十K．K．K。＝＜ l一 11—K。IK。X。＜l 理论分析和数值计算表明：采用这种控制器可以将系统控制到稳定的极限环、ZP、3P等系 统自身的周期轨道。该方法也可以用于其他超混饨系统的控制研究。更多还原

【Abstract】 In the recent two decades, the research of synchronization and control of chaotic system attracts more attention and interest among people, and it shows wonderful achievements in many fields, relevant content are given in this thesis in brief. Firstly, it introduces the characters of chaos and the means to identify chaotic system, then some methods about synchronization and control of chaos are introduced, basing on some of the methods, this thesis proposes some new improved methods to study the 4D oscillator hyperchaotic system on synchronization and control, and it gets wonderful results.The 4D oscillator circuit is simple and easy to realize in reality, which shows complicated dynamic character, and it is a hyperchaotic system, it will show great value to study and research the synchronization and control of this hyperchaotic system. For this model, this thesis shows my works in the following parts:(1 ) It uses a gain function Kc (t) to equal the disadvantages effect of a common signal channel on the transmitted signal , considering the fact that signal may become distorted when it transform from one place to another place, the chaotic signal x1 and a standard direct current signal S(r) aresent through the same common signal channel, which become the distorted signal Kc(t)xi(t) and Kc(t)s(t), it can restore the real signal by using a self-adaptive compensator equipped at the front part of the receiving system, the gain of compensator is Kr , basing on the literature[115-116], this thesis gets news K r and it can be showed as the following equation:the value can be get from the following equation : The numerical simulation result shows :it can restore the distorted signal with the gain Kr proposed in this paper.(2) Using the method of parameter identification in literature [117-118], selecting gain function:giving the initial value of the parameter observer from the time serial of output variables of the system, the numerical simulation result shows that the parameter observer proposed in this paper can identify the unknown parameters of the system quickly and exactly no matter if the parameters keep invariable or change in some rule, and the identifying speed is faster than the method in [117-118], when the unknown parameters are being identified ,\vith parameter compensator, it can synchronizes two hyperchaotic systems completely even if some parameters mismatch.( 3 ) Basing on the stability theory, constructing the following Lyapunov function.it gets the controller with the same method, it can get therelevant controllers when parameters mismatch. The numerical simulation result shows that the controller proposed in this paper can synchronize two hyperchaotic system completely.( 4 ) Basing on the result [82 , 104] , which synchronization can be reached by using occasional driving or feedback filter, the following controllers are proposed in this thesis to synchronize two 4D oscillator hyperchaotic systems.The numerical results show that it can synchronize two hyperchaotic systems completely no matter if the parameters match or not.(5) Using the method APD ,it select a new drive signal S =x1- cx3 to synchronize the response system, the theory analysis and numerical simulation results show that it can synchronize two hyperchaotic systems completely with the drive signal S =x1- cx3, comparing with themethod of selecting signal in literature [114] , with the drive signal S =x1- cx3 , it can shortens the transient period of synchronization(6) Using the outside standard signal to control 4D oscillator hyperchaotic system, Basing on the stability theory, constructing the following Lyapunov function it gets the controller as following:The theory analysis and numerical simulation result show: using the controller above ,it can control the system to reach any desired stable point and period orbit. Basing on the stability theory, selecting controller as following:The theory analysis and numerical simulation result s更多还原