耦合时滞复杂网络同步控制及应用

发布时间：2018-03-14 18:31

本文选题：复杂网络　切入点：同步控制　出处：《浙江大学》2015年博士论文　论文类型：学位论文

【摘要】：复杂网络广泛存在于自然界、社会生活和工程系统中,受到了来自各学科、各领域专家学者的广泛关注。复杂网络是许多复杂系统的高度抽象系统,由多个节点和连接节点的边组成,节点代表某个具体的动态特性或者子系统,边代表它们之间的关系。同步现象普遍存在于各种复杂系统中,是复杂网络典型的集体行为之一,是许多复杂系统合作的基础。复杂网络同步问题的研究不仅有助于人们认识自然界中一些自然现象形成的原因,而且还能为现实中许多复杂大系统相关问题提供新的思路和方法,具有广阔的应用前景,因此对复杂网络同步控制问题的研究具有重要的理论意义和现实意义。本文主要基于Lyapunov稳定性理论、矩阵论、控制论、图论和线性矩阵不等式(LMI)等理论,研究了几类耦合时滞复杂网络的同步控制问题,本文的主要工作包括以下几个方面：1) 基于Lyapunov-Krasovskii稳定性理论和线性矩阵不等式工具,研究了具有lur'e非线性特征和拓扑切换的耦合时滞复杂网络的同步稳定性分析与控制问题,得到了切换时滞复杂网络全局渐近同步稳定的充分条件和控制器设计准则。在基于线性矩阵不等式形式的同步稳定性判据和控制器设计准则中,为了降低引入矩阵Kronecker积带来的计算复杂度,采用了特征值分解和凸组合方法,降低了判据和准则的决策变量个数,降低了结果计算复杂度。2) 采用Lyapunov-Krasovskii稳定性理论和矩阵不等式方法,研究了含外部干扰和拓扑连接权值时变的耦合时滞复杂网络同步稳定性分析与控制问题,得到了误差系统绝对稳定且具有H∞性能指标上界的充分条件和同步控制器设计准则。在同步稳定性判据和控制器设计准则中,采用特征值分解、Weyl不等式和凸组合等方法,有效解决了计算复杂度和拓扑连接矩阵区间内时变的问题,使判据可以采用LMI工具求解,并降低了其计算复杂度。3) 研究了含异质节点和拓扑连接强度时变的耦合时滞复杂网络同步控制问题,采用前馈控制与误差反馈控制相结合的思想,设计了两种有效的混合控制策略,其中前馈控制补偿节点与目标的结构差异,反馈控制保证系统稳定,然后利用Lyapunov-Krasovskii稳定性理论推导了同步控制策略的可行性和参数设计准则。4) 在含异质节点的复杂网络中,考虑各节点有不同的目标,提出了自同步概念。基于前馈补偿和反馈控制的思想,对不含耦合时滞和含耦合时滞的异质复杂网络,分别设计了两种自同步混合控制器,并通过Lyapunov稳定性理论推导了同步控制策略的可行性,得到了控制器参数设计准则。5) 将网络环境下二阶非线性多智能体系统的一致问题建模成耦合时滞复杂网络的同步问题,研究了复杂网络同步控制理论在二阶多智能体系统一致性控制中的应用,得到了网络环境下二阶非线性多智能体一致性判据和控制方案。6) 探索了复杂网络同步控制理论在复杂供应网络中的相关应用,建立复杂供应网络数学模型,利用耦合时滞复杂网络同步稳定性理论,设计了一种调整各节点生产率的控制策略,保证复杂供应网络稳定工作在理想状态。
[Abstract]:Complex networks exist widely in nature, social life and engineering system, by the extensive attention from different disciplines, experts and scholars in various fields. The complex network is a highly abstract system of many complex systems, composed of a plurality of nodes and edges connecting nodes, nodes represent a specific dynamic characteristics or subsystem, the edges represent the relationship between them. The synchronization phenomenon exists in a variety of complex system, collective behavior is one of the typical complex networks is the foundation of many complex systems of cooperation. The research on synchronization of complex network can not only help people understand reasons for the formation of some natural phenomena in nature, but also provide new ideas and methods for related problems in reality, many complex systems, has broad application prospects, therefore the research of synchronization control of complex networks has important theoretical significance and practical significance Meaning. This paper mainly Lyapunov stability theory, based on the matrix theory, control theory, graph theory and linear matrix inequality (LMI) theory, synchronous control problem on several types of complex dynamical networks with coupling delays, the main work of this paper includes the following aspects: 1) the Lyapunov-Krasovskii stability theory and linear matrix inequality based on the analysis and control problem study on the stability of synchronization coupling delays with Lur'e nonlinear and complex network topology, the switching delay complex network global asymptotic synchronization stable sufficient conditions and controller design. Based on the criteria in the form of linear matrix inequalities synchronous stability criterion and controller design standards, in order to reduce the matrix Kronecker product brings complexity, by eigenvalue decomposition and convex combination method, reduces the number of decision variables and the criterion criterion, reduction The results of low computational complexity.2) using the Lyapunov-Krasovskii stability theory and matrix inequality method, the analysis and control of synchronization of complex networks with coupling delay stability of external disturbance and time-varying topology connection weights, the system error and absolute stability with sufficient conditions of robust H design criteria for the upper bound of the performance index and synchronous controller. Synchronous stability criterion and controller design criterion, using eigenvalue decomposition, Weyl inequality and convex combination method effectively solves the computational complexity and topology matrix interval time-varying problem, the criterion can be solved by LMI tools, and reduces the computational complexity of the synchronization control problem of.3) coupled with heterogeneous nodes and topology connection strength of complex network, feedforward control and error feedback control of the idea of combining two kinds of design Hybrid control strategy is effective, the structural differences between the feedforward control node and the target, the feedback control to ensure the stability of the system, and then using the Lyapunov-Krasovskii stability theory is used to deduce the synchronization control strategy design criteria and feasibility of parameter.4) in heterogeneous nodes containing complex networks, considering each node have different goals, put forward the concept of self synchronization feedforward and feedback control. Based on the idea of free coupling delays and heterogeneous complex networks with coupling delays, respectively designed two kinds of self synchronous hybrid controller, and through the Lyapunov stability theory the feasibility of synchronous control strategy, the design criterion of.5 controller parameters) will be consistent with the two order nonlinear multi intelligence body system under network environment is modeled as the synchronization of complex dynamical networks with coupling delays, we study the synchronization control theory in two order complex networks The application of intelligent control system, obtained.6 two order nonlinear multi-agent consistency criterion and control scheme under the network environment) explores the synchronization control of complex network theory in complex supply network, the establishment of complex supply network model, the use of coupled time-delay complex network synchronization stability theory and design a control strategy for adjusting the node productivity, ensure complex supply network stability in the ideal state.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O157.5;O231

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