基于分数阶控制器的复杂网络同步控制研究

发布时间：2018-03-03 09:21

本文选题：复杂网络　切入点：分数阶微分系统　出处：《安徽大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着信息技术的发展,复杂网络已被广泛应用于描述各种人工和自然系统,如社交网络,互联网,神经网络,生物网络。复杂网络是21世纪重点研究课题之一,吸引了大量不同领域的研究人员,建立了一些经典的网络模型来描述现实生活中各类真实的复杂系统。深入研究复杂网络对更好地理解各类真实复杂系统具有非常重大的现实意义。同步作为复杂网络主要的动力学行为,一直备受研究者的青睐。复杂网络同步的早期研究只针对整数阶微分系统节点,而分数阶微分系统能够更好的描述现实网络中具有的记忆属性,因而对于分数阶复杂网络同步控制研究已经成为了新的研究课题。本文基于Lyapunov稳定性理论、非线性分数阶稳定性理论和LaSalle不变性原理分析了两个耦合分数阶复杂网络的混合同步问题。通过引入分数阶控制器,使得具有分数阶混沌或超混沌节点的两个耦合复杂网络达到混合同步状态。并提出了实现包括驱动-响应网络外同步和每一个网络内同步的充分条件。结合理论分析和仿真实验验证出,在系统参数满足特定的条件下,两个耦合网络可以达到混合同步状态。此外,本文关注由分数阶混沌系统为节点构成的两个耦合分数阶复杂网络的投影同步问题,利用非线性分数阶稳定性理论和自适应控制策略,在响应网络中添加分数阶控制器,实现了驱动-响应网络的投影同步。全文的主要内容和创新点如下:(1)利用分数阶微积分定义,深入研究分数阶微分系统所构成的复杂网络。在分数阶复杂网络同步研究中,考虑到阶数对系统控制作用的影响,选用控制参数为分数阶微分形式的控制器,并通过实验验证了此控制器的有效性。(2)针对驱动-响应分数阶复杂网络的混合同步进行了详细阐述。复杂网络中包含大量相互作用的节点,网络的拓扑结构直接影响单个复杂网络的内同步,两个不同复杂网络之间的外同步更多地依赖于系统中的控制器。本文利用分数阶非线性稳定性理论、Lyapunov稳定性理论及LaSalle不变性原理,给出了两个耦合分数阶复杂网络混合同步的充分条件。最后,通过分数阶超混沌Lorenz、混沌Lorenz和超混沌Chen系统的数值仿真验证了理论结果的正确性。(3)分析了两个耦合分数阶复杂网络的投影同步问题。根据投影同步定义,利用分数阶非线性稳定性理论和自适应控制技术,设计出分数阶控制器,在该控制器的作用下实现了驱动-响应网络的投影同步。最后,通过分数阶混沌Lorenz、分数阶混沌Liu和分数阶混沌Chen系统的数值仿真对投影同步控制效果进行了验证。
[Abstract]:With the development of information technology, complex networks have been widely used to describe various artificial and natural systems, such as social networks, the Internet, neural networks, biological networks. Attracted a lot of researchers from different fields, Some classical network models are established to describe various real complex systems in real life. It is very important to study complex networks for better understanding of real complex systems. Synchronization is a complex system. The main dynamic behavior of the network, The early research on synchronization of complex networks is focused on the nodes of integer-order differential systems, and fractional differential systems can better describe the memory properties of real networks. Therefore, the research of fractional complex network synchronization control has become a new research topic. This paper based on Lyapunov stability theory, Nonlinear fractional stability theory and LaSalle invariance principle are used to analyze the mixed synchronization problem of two coupled fractional order complex networks. Two coupled complex networks with fractional chaotic or hyperchaotic nodes reach the state of mixed synchronization. Sufficient conditions for the realization of external synchronization including drive-response network and synchronization within each network are proposed. The theory is combined with the theory. The analysis and simulation results show that, Under the condition that the system parameters satisfy certain conditions, two coupled networks can achieve mixed synchronization state. In addition, this paper focuses on the projective synchronization problem of two coupled fractional order complex networks composed of fractional chaotic systems as nodes. Using nonlinear fractional stability theory and adaptive control strategy, a fractional order controller is added to the response network. The projective synchronization of drive-response network is realized. The main contents and innovations of this paper are as follows: 1) by using the fractional calculus definition, the complex network formed by fractional differential system is deeply studied. In the research of fractional order complex network synchronization, Considering the influence of order number on the control of the system, the control parameter is chosen as the controller in fractional differential form. The effectiveness of the controller is verified by experiments. (2) the hybrid synchronization of drive-response fractional complex networks is described in detail. The complex networks contain a large number of interacting nodes. The topology of the network directly affects the internal synchronization of a single complex network. The external synchronization between two different complex networks is more dependent on the controller in the system. In this paper, the fractional order nonlinear stability theory and the LaSalle invariance principle are used. Sufficient conditions for hybrid synchronization of two coupled fractional-order complex networks are given. Finally, Numerical simulation of fractional hyperchaos, chaotic Lorenz and hyperchaotic Chen system verifies the correctness of the theoretical results. The projection synchronization problem of two coupled fractional order complex networks is analyzed, according to the definition of projection synchronization. Based on fractional nonlinear stability theory and adaptive control technology, a fractional order controller is designed. The projective synchronization of driving-response network is realized under the action of the controller. Finally, The effect of projection synchronization control is verified by numerical simulation of fractional chaotic Lorenz, fractional chaotic Liu and fractional chaotic Chen system.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;O231

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