混沌系统泛化函数投影同步控制研究

发布时间：2018-07-05 09:45

本文选题：泛化函数投影同步 + 自适应同步　；参考：《大连理工大学》2015年博士论文

【摘要】：混沌系统具有复杂而独特的动力学特征,其在许多科学领域都有着很大的应用潜力.目前对混沌同步控制的研究已成为国际上的热点.其中混沌投影同步是一种重要的同步方式,实现同步时,驱动系统状态与响应系统状态依某比例因子演化.国内外许多学者将比例因子扩展成对角矩阵、函数以及函数矩阵等,得到了各种类型的投影同步方式.这些扩展增大了投影同步的适用范围,增强了其应用的灵活性.本文考虑驱动系统和响应系统之间存在某种“位移”的情形,提出了混沌泛化函数投影同步的概念,并应用自适应控制方法实现了参数未知混沌系统的泛化函数投影同步.针对混沌系统存在不确定性时的泛化函数投影同步问题,分别设计了主动变论域自适应模糊控制器和快速终端滑模控制器.基于模糊推理建模方法,定义了一类新的混沌系统—HX型混沌系统,并应用并行分布补偿技术实现了其泛化函数投影同步.考虑到时间延迟的存在,提出了泛化函数投影延迟同步的概念,并给出了积分滑模控制策略.具体工作及结果总结如下：1.考虑到驱动系统和响应系统之间存在某种“位移”的情形,我们定义了混沌系统的泛化函数投影同步的概念,进一步推广了混沌投影同步的概念.这种“位移”是由一个参考系统的状态来表示的.这个参考系统可以是常向量、周期系统、拟周期系统、混沌系统或超混沌系统以及它们的组合.通过调节参考系统和函数尺度因子矩阵,泛化函数投影同步可以退化为完全同步、反同步、投影同步、修正同步、函数投影同步和修正函数投影同步等同步方式.针对含未知参数的混沌系统的泛化函数投影同步,我们提出了自适应控制方法,并采用Lyapunov稳定性理论论证了其合理性,分别对常向量、函数向量、超混沌系统、含未知参数的超混沌系统这四种参考系统意义下的混沌泛化函数投影同步进行研究.仿真结果证实了控制策略的有效性.2.基于产生超混沌系统的三个必要条件,在Lorenz系统基础上构造了一个具有收敛直线的超混沌系统.我们对该系统的耗散性、平衡点、分岔图、Lyapunov指数、Lyapunov维数及Poincare截面等进行了研究,指出该系统仅有一个平衡点,并且指出在一定的参数条件下系统呈现周期、拟周期、混沌及超混沌等动力学性态.在较大的参数区间内,这个系统是超混沌的.针对构造的超混沌系统带有不确定性时的泛化函数投影同步问题,我们提出了主动变论域自适应模糊控制方法.以超混沌Liu系统作为参考系统进行仿真,结果证实了控制策略的有效性.3.通过在Loreng系统的第二个方程之上增加一个反馈项,我们构造了一个有三个平衡点的四维自治系统.分析了其耗散性、吸引子的存在性、平衡点、分岔图、Lyapunov指数等非线性特征.通过Lyapun ov指数谱可以发现该系统具有丰富的动态特性.在参数变化的一个大的范围内,系统是超混沌的.对于带有不确定性的混沌系统的泛化函数投影同步,我们提出了快速终端滑模控制方法.以该新超混沌系统与超混沌Chen系统分别作为驱动系统和响应系统,对其泛化函数投影同步进行仿真研究,结果证实了所述控制方法的有效性.4.对于右端为多项式的混沌系统,我们采用逐项模糊推理建模再进行线性叠加的方法,得到其HX方程组.通过分析,发现这样的HX方程组并非每一项都是变系数的,甚至一些系统的HX方程组与原混沌系统相同.对于混沌(超混沌)系统的HX方程组,若其为变系数的,由模糊系统的万能逼近性,在适当的模糊划分下,其为混沌(超混沌)系统,称之为HX型混沌(超混沌)系统.这样我们就通过现有混沌(超混沌)系统得到新的混沌(超混沌)系统.可以通过简单的改变模糊划分来改变HX型混沌(超混沌)系统的系数,实现混沌切换.我们通过逐片精确T-S模糊建模再组合的方法,得到了四维HX型超混沌系统的精确T-S模糊模型,逐片应用并行分布补偿(PDC)技术实现了HX型超混沌系统的泛化函数投影同步.5.考虑到现实控制工程中时间延迟的客观存在,我们提出了泛化函数投影延迟同步的概念.这拓展了修正函数延迟投影同步和泛化函数投影同步,其应用范围更广泛.分别应用主动滑模控制方法和主动模糊滑模控制方法对带有不研究性超混沌系统的泛化函数投影延迟同步进行了研究.
[Abstract]:Chaotic systems have complex and unique dynamic characteristics, and they have great potential in many fields of science. At present, the research of chaotic synchronization control has become a hot spot in the world. Chaotic projection synchronization is an important synchronization mode. When the synchronization is realized, the state of the drive system and the state of the response system are proportional to a certain factor. Many scholars at home and abroad extend the proportion factor into diagonal matrix, function and function matrix, and get various types of projection synchronization. These extensions increase the scope of application of the projection synchronization and enhance the flexibility of its application. The concept of projection synchronization of chaotic generalization function is presented, and an adaptive control method is applied to realize the projection synchronization of the generalization function of the unknown chaotic system. The adaptive fuzzy controller and the fast terminal sliding mode controller are designed for the problem of the projection synchronization of the generalization function in the uncertainty of the chaotic system. In the fuzzy reasoning modeling method, a new chaotic system - HX type chaotic system is defined, and the generalization function projection synchronization is realized by the parallel distribution compensation technology. Considering the existence of time delay, the concept of the generalized function projection delay synchronization is proposed, and the product partition sliding mode control strategy is given. The specific work and the results are summarized as follows. 1.: considering the existence of some "displacement" between the driving system and the response system, we define the concept of the projection synchronization of the generalization function of the chaotic system, and further generalized the concept of chaotic projection synchronization. This "displacement" is shown by the state of a reference system. This reference system can be a constant vector, a week. Phase system, quasi periodic system, chaotic system or hyperchaotic system and their combination. By adjusting the reference system and function scale factor matrix, the generalization function projection synchronization can degenerate into complete synchronization, anti synchronization, projection synchronization, modified synchronization, function projection synchronization and modified function projection synchronization. The generalization function of a number of chaotic systems is projected synchronously. We propose an adaptive control method, and demonstrate its rationality by using the Lyapunov stability theory, and study the projection synchronization of the chaotic generalization function under the meaning of four reference systems, such as constant vector, function vector, hyperchaotic system and hyperchaotic system with unknown parameters. The true results confirm the effectiveness of the control strategy.2. based on three necessary conditions for the generation of hyperchaotic systems. On the basis of the Lorenz system, a hyperchaotic system with convergent straight lines is constructed. We have studied the system's dissipation, equilibrium point, bifurcation diagram, Lyapunov index, Lyapunov dimension and Poincare cross section. The system has only one equilibrium point, and points out that under certain parameter conditions, the system presents the dynamic state of periodic, quasi periodic, chaotic and hyperchaos. In the larger parameter range, this system is hyperchaotic. We propose an active variable theory for the projection synchronization of the generalization function when the hyperchaotic system with the structure is uncertain. The domain adaptive fuzzy control method is simulated with the hyperchaotic Liu system as a reference system. The results confirm the effectiveness of the control strategy.3. by adding a feedback item over the second equations of the Loreng system. We construct a four dimensional autonomous system with three equilibrium points. The dissipation and existence of the attractor are analyzed. The nonlinear characteristics of the equilibrium point, the bifurcation diagram, the Lyapunov exponent and so on. Through the Lyapun ov exponent spectrum, it is found that the system has rich dynamic characteristics. In a large range of parameter changes, the system is hyperchaotic. For the generalization function projection synchronization with uncertain chaotic systems, we propose a fast terminal sliding mode controller. Method. Using the new hyperchaotic system and hyperchaotic Chen system as the driving system and the response system respectively, the simulation of the projection synchronization of its generalization function is studied. The results prove that the effectiveness of the control method.4. is a chaotic system with polynomial on the right end. Through the analysis of the HX equations, it is found that such HX equations are not all variable coefficients, and even some system HX equations are the same as those of the original chaotic system. For the HX equations of the chaotic (hyperchaos) system, if it is a variable coefficient, the universal compel of the fuzzy system is chaotic (hyperchaos) under proper fuzzy division. The system is called HX chaotic (hyperchaos) system. In this way, we can get new chaotic (hyperchaos) system through the existing chaotic system. We can change the coefficients of the HX chaotic (hyperchaos) system by simply changing the fuzzy partition to realize the chaotic switching. We get the method of combining the exact T-S fuzzy modeling by piece by piece. To the exact T-S fuzzy model of the four dimensional HX hyperchaotic system, the piecewise application parallel distribution compensation (PDC) technology is used to realize the generalization function projection synchronization.5. of HX hyperchaos system, which takes into account the objective existence of time delay in the real control project. We propose the concept of the delay synchronization of the generalization function. This extends the modified function extension. The application scope of the delayed projection synchronization and the generalization function projection is more extensive. The active sliding mode control method and the active fuzzy sliding mode control method are applied to the generalization function projection delay synchronization with the non research hyperchaos system respectively.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O415.5;O231

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