时滞神经网络的Hopf分岔与多智能体系统的一致性
发布时间：2019-03-05 08:32
【摘要】：首先,简述了复杂网络,时滞系统,分岔和多智能体系统的基本概念、研究背景和研究意义以及本论文的主要内容和创新性工作。其次,考虑了两种时滞神经网络的Hopf分岔问题,一种是含有七个神经元和七个时滞的BAM神经网络,另一种是含有2n个神经元的神经网络。这两种模型都是第一次被分析,对丰富和促进神经网络的发展具有一定的意义。另外,由于它们都含有较多的神经元和较多的时滞,所以它们更加接近现实,更加有利于理解现实中的神经网络。主要研究方法是:以部分时滞的和作为分岔参数,通过分析对线性化后系统的特征方程,获得了使系统产生分岔的参数临界值以及使系统产生分岔的充分条件。更深入的是,对于第一种模型,通过利用中心流形定理和正规型法则,分析了其Hopf分岔的稳定性和方向,以及分岔周期的部分性质。然后,一类二阶线性多智能体系统的一致性问题被分析和研究,每个智能体都有自身的速度和位置两个变量,在设计的一致协议下,每个智能体随着时间的推移逐渐趋于同一种状态。随后,线性的和非线性的两种多智能体系统被分别研究。对于线性系统,设计了一种简化的一致性协议,该协议使得智能体之间的复杂信息交流被限制在一棵有向生成树中。对于非线性系统,设计了一种含有反馈增益的一致性协议,该协议使得每一个智能体的运行状态都要受到其自身状态的影响。通过相应的推导计算获得了比其他某些文献中更加优越的一致性条件。它们的研究方法是:设计一致性协议,利用图论和矩阵的一些性质推导计算,获得使误差系统在原点稳定的条件。线性系统系数矩阵的特征值的实部是否都为负是判断该系统是否稳定的重要条件。对于非线性系统,判断其稳定的主要方法是李雅普诺夫第二方法,即通过构造V函数来进行判断。最后,对本论文所做的工作进行了总结以及对未来工作的研究方向进行了说明。
[Abstract]:Firstly, the basic concepts, research background and significance of complex networks, time-delay systems, bifurcation and multi-agent systems, as well as the main contents and innovative work of this paper are briefly introduced. Secondly, the Hopf bifurcation problem of two kinds of time-delay neural networks is considered, one is BAM neural network with seven neurons and seven delay, the other is the neural network with 2n neurons. These two models have been analyzed for the first time, which have a certain significance to enrich and promote the development of neural networks. In addition, they all contain more neurons and more time-delay, so they are closer to reality and more conducive to understanding the real-world neural network. The main research methods are as follows: taking the sum of partial delay as the bifurcation parameter, by analyzing the characteristic equation of the linearized system, the critical value of the parameter of the system and the sufficient conditions for the bifurcation of the system are obtained. Furthermore, for the first model, the stability and direction of the Hopf bifurcation and some properties of the bifurcation period are analyzed by using the central manifold theorem and the rule of normal type. Then, the consistency problem of a class of second-order linear multi-agent systems is analyzed and studied. Each agent has its own two variables of speed and position. Each agent gradually tends to the same state over time. Subsequently, two kinds of multi-agent systems, linear and nonlinear, are studied respectively. For linear systems, a simplified consistency protocol is designed, which limits the communication of complex information between agents to a directed spanning tree. For nonlinear systems, a consistency protocol with feedback gain is designed, which makes the operation state of each agent affected by its own state. Through the corresponding derivation and calculation, better consistency conditions are obtained than those in some other literatures. Their research methods are as follows: the consistency protocol is designed, some properties of graph theory and matrix are used to derive and calculate, and the conditions to make the error system stable at the origin are obtained. Whether the real part of the coefficient matrix of a linear system is negative or not is an important condition to determine whether the system is stable or not. For nonlinear systems, the main method for judging the stability of nonlinear systems is Lyapunov's second method, that is, by constructing a V function to judge the stability of nonlinear systems. Finally, the work of this paper is summarized and the research direction of the future work is explained.
【学位授予单位】：青岛科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2434713
[Abstract]:Firstly, the basic concepts, research background and significance of complex networks, time-delay systems, bifurcation and multi-agent systems, as well as the main contents and innovative work of this paper are briefly introduced. Secondly, the Hopf bifurcation problem of two kinds of time-delay neural networks is considered, one is BAM neural network with seven neurons and seven delay, the other is the neural network with 2n neurons. These two models have been analyzed for the first time, which have a certain significance to enrich and promote the development of neural networks. In addition, they all contain more neurons and more time-delay, so they are closer to reality and more conducive to understanding the real-world neural network. The main research methods are as follows: taking the sum of partial delay as the bifurcation parameter, by analyzing the characteristic equation of the linearized system, the critical value of the parameter of the system and the sufficient conditions for the bifurcation of the system are obtained. Furthermore, for the first model, the stability and direction of the Hopf bifurcation and some properties of the bifurcation period are analyzed by using the central manifold theorem and the rule of normal type. Then, the consistency problem of a class of second-order linear multi-agent systems is analyzed and studied. Each agent has its own two variables of speed and position. Each agent gradually tends to the same state over time. Subsequently, two kinds of multi-agent systems, linear and nonlinear, are studied respectively. For linear systems, a simplified consistency protocol is designed, which limits the communication of complex information between agents to a directed spanning tree. For nonlinear systems, a consistency protocol with feedback gain is designed, which makes the operation state of each agent affected by its own state. Through the corresponding derivation and calculation, better consistency conditions are obtained than those in some other literatures. Their research methods are as follows: the consistency protocol is designed, some properties of graph theory and matrix are used to derive and calculate, and the conditions to make the error system stable at the origin are obtained. Whether the real part of the coefficient matrix of a linear system is negative or not is an important condition to determine whether the system is stable or not. For nonlinear systems, the main method for judging the stability of nonlinear systems is Lyapunov's second method, that is, by constructing a V function to judge the stability of nonlinear systems. Finally, the work of this paper is summarized and the research direction of the future work is explained.
【学位授予单位】：青岛科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关期刊论文 前1条
1 陈阳舟;盖彦荣;张亚霄;;线性多智能体系统一致性问题的部分稳定性方法（英文）[J];自动化学报;2014年11期
，本文编号：2434713
本文链接：https://www.wllwen.com/kejilunwen/yysx/2434713.html
