分数阶耦合网络的稳定性和同步控制

发布时间：2017-12-31 21:20

本文关键词：分数阶耦合网络的稳定性和同步控制　出处：《新疆大学》2016年博士论文　论文类型：学位论文

【摘要】：分数阶微积分作为整数阶微积分在阶数上的延伸和推广,其在物理、化学、生物、电子工程和经济等诸多领域表现出强大的优势和广泛的应用前景,引起了国内外学者的广泛关注,已成为当前的研究热点,尤其是分数阶耦合网络的稳定性和同步控制的研究.本文主要包含三部分内容:分数阶耦合网络稳定性问题;分数阶复杂网络的同步控制问题;分数阶神经网络的同步控制与参数识别.具体的研究工作如下:第一部分,考虑了三类分数阶耦合网络的稳定性问题.(1)研究了一类没有控制的分数阶耦合网络的稳定性问题.应用Kirchhoff矩阵树定理,我们对这类耦合网络给出了一种构造Lyapunov函数的方法.通过结合图理论和Lyapunov方法,得到了耦合网络稳定、一致稳定和一致渐近稳定的充分条件.最后,通过数值仿真验证了所得理论结果的正确性.(2)研究了一类具有反馈控制的分数阶耦合网络的全局Mittag-Leffler稳定性.基于压缩映射原理,得到一些充分条件确保了耦合网络平衡点的存在性和唯一性.通过使用Lyapunov方法、图理论和一些有用的不等式,给出了网络全局Mittag-Leffler稳定的判别准则.最后,数值模拟验证了理论结果的正确性并且展示了分数阶和反馈控制对所考虑系统解的影响.(3)研究了一类具有反馈控制的脉冲分数阶耦合网络.通过结合图理论和Lyapunov方法,得到了系统全局渐近稳定和全局Mittag-Leffler稳定的充分条件,这些条件与网络的拓扑性质有密切的关系.最后,通过数值模拟证明了所得理论结果的正确性和有效性.第二部分,研究了一般的分数阶复杂网络在周期间歇性牵制控制下的全局同步.通过引入周期间歇牵制控制策略,运用Lyapunov稳定性理论和一些分析技巧,得到了网络同步的判别准则.数值模拟验证了理论结果的正确性和有效性.第三部分,研究了具有未知参数的分数阶神经网络的同步和参数识别.首先,把众所周知的Barbalat引理推广到分数阶情况.基于推广的Barbalat引理和一些分析技巧,在自适应控制器和参数识别规则下,可以实现神经网络的同步和参数识别.理论证明和数值模拟验证了所提方法的有效性.
[Abstract]:As an extension and extension of integral order calculus in order, fractional calculus has shown great advantages and wide application prospects in many fields such as physics, chemistry, biology, electronic engineering and economy. It has attracted the attention of scholars both at home and abroad and has become a hot research topic. Especially the research on the stability and synchronization control of fractional coupled networks. This paper mainly includes three parts: the stability of fractional coupled networks; Synchronization control of fractional complex networks; The synchronization control and parameter identification of fractional neural networks. The specific research work is as follows: the first part. In this paper, we consider the stability problem of three kinds of fractional coupled networks. We study the stability of a class of fractional coupled networks without control. The Kirchhoff matrix tree theorem is applied. We give a method of constructing Lyapunov function for this kind of coupling network. By combining graph theory with Lyapunov method, we obtain the stability of the coupled network. Sufficient conditions for uniformly stable and uniformly asymptotically stable. The correctness of the theoretical results is verified by numerical simulation. The global Mittag-Leffler stability of a class of fractional coupled networks with feedback control is studied based on the contraction mapping principle. Some sufficient conditions are obtained to ensure the existence and uniqueness of the equilibrium point of the coupled network. By using the Lyapunov method, the graph theory and some useful inequalities are obtained. The criterion of global Mittag-Leffler stability is given. Finally. Numerical simulation verifies the correctness of the theoretical results and shows the effects of fractional order and feedback control on the solution of the system under consideration. A class of impulsive fractional order coupled networks with feedback control is studied by combining graph theory and Lyapunov method. Sufficient conditions for global asymptotic stability and global Mittag-Leffler stability of the system are obtained. These conditions are closely related to the topological properties of the network. The correctness and validity of the theoretical results are proved by numerical simulation. Part two. The global synchronization of general fractional order complex networks under periodic intermittent control is studied. By introducing periodic intermittent control strategy, Lyapunov stability theory and some analytical techniques are used. The discriminant criterion of network synchronization is obtained, and the correctness and validity of the theoretical results are verified by numerical simulation. In the third part, the synchronization and parameter identification of fractional neural networks with unknown parameters are studied. The well-known Barbalat Lemma is extended to fractional order cases. Based on the generalized Barbalat Lemma and some analytical techniques, the adaptive controller and parameter identification rules are used. The synchronization and parameter identification of neural network can be realized, and the validity of the proposed method is verified by theoretical proof and numerical simulation.
【学位授予单位】：新疆大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O231

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