多互联复杂动态网络一致性分析与控制

发布时间：2018-05-21 11:06

本文选题：一致性 + 多互联系统　；参考：《北京工业大学》2016年硕士论文

【摘要】：复杂性和复杂网络是当今科学界重点研究的课题之一,其将复杂系统概括为由相互作用的多个节点组成的网络系统。其中一致性是复杂动态网络中典型的集体行为,也是复杂网络最重要的动力学特性之一。所谓一致性问题是指如何基于局部信息交换的多智能体系统达到状态一致。在控制领域中,多智能体系统一致性问题是协调控制的重要问题之一。本文针对动态网络系统的一致性问题进行了研究,考虑了多智能体间多通讯对应的多互联动态网络系统在固定拓扑、马尔科夫随机跳变拓扑下的一致性问题,给出了系统的一致性判据,且设计了静态输出反馈控制器。主要工作包括以下几个方面:(1)针对状态互联和控制器互联的多互联动态网络线性系统进行一致性分析与控制。基于部分变元稳定性理论,利用线性变换矩阵对线性网络系统进行处理将系统一致性问题转换成部分稳定性问题。在状态互联与控制器互联结构相同情况下,将所得大系统的部分稳定性问题分解成几个独立的线性系统稳定性问题,采用Lyapunov方法和投影定理得到了基于LMI的一致性判据,且通过此判据可得到静态输出反馈控制器参数。进一步,考虑了带有互联参数不确定性的线性动态网络系统的一致性问题。给出了基于LMI的一致性判据及静态输出反馈控制器的设计方法。(2)考虑线性互联和非线性互联的多互联非线性动态网络系统的一致性问题。节点系统是Lure型的非线性系统。采用(1)中的线性变换矩阵将非线性网络系统的一致性问题转换成部分稳定性问题。基于圆判据得到了整个网络系统一致的频域判据,再运用KYP引理和Schur补引理给出了基于LMI的时域判据,提出了静态输出反馈控制器的设计方法。同时研究了系统具有互联参数不确定性和非线性参数不确定性的一致性问题。得到了相应的频域判据、基于LMI的时域判据及静态输出反馈控制器的设计方法。(3)对具有通信时滞、马尔科夫随机跳变拓扑的多互联动态网路系统,进行一致性分析与控制。其中考虑连续的马尔科夫链转移速率矩阵是含有部分未知元素。首先应用(1)中的线性变换矩阵对网络系统一致性问题进行转换,其次对每个模态下的系统,选择适当的Lyapunov-Krasovskii泛函分别得到线性系统和非线性系统的基于双线性矩阵不等式的一致性判据,并且通过迭代算法得到静态输出反馈控制器增益。
[Abstract]:Complexity and complex network is one of the most important research topics in the scientific community nowadays, which generalizes the complex system into a network system composed of multiple nodes of interaction. Consistency is a typical collective behavior in complex dynamic networks, and it is also one of the most important dynamic characteristics of complex networks. The so-called consistency problem refers to how to achieve state consistency in a multi-agent system based on local information exchange. In the field of control, the consistency of multi-agent system is one of the important problems of coordinated control. In this paper, the consistency problem of dynamic network systems is studied, and the consistency problem of multi-interconnected dynamic network systems corresponding to multi-agent communication under fixed topology and Markov random jump topology is considered. The consistency criterion of the system is given, and the static output feedback controller is designed. The main work includes the following aspects: (1) Conformance analysis and control for multi-interconnected dynamic linear network systems with state interconnection and controller interconnection. Based on the partial argument stability theory, the linear transformation matrix is used to deal with the linear network system. The consistency problem of the system is transformed into the partial stability problem. In the case of the same structure of state interconnection and controller interconnection, the partial stability problem of large scale system is decomposed into several independent linear system stability problems. The consistency criterion based on LMI is obtained by using Lyapunov method and projection theorem. The static output feedback controller parameters can be obtained by this criterion. Furthermore, the consistency problem of linear dynamic network systems with interconnected parameter uncertainty is considered. The consistency criterion based on LMI and the design method of static output feedback controller are given. The node system is a nonlinear system of Lure type. The consistency problem of the nonlinear network system is transformed into a partial stability problem by using the linear transformation matrix in this paper. Based on the circle criterion, the consistent frequency domain criterion of the whole network system is obtained. Then the time-domain criterion based on LMI is given by using KYP Lemma and Schur complementary Lemma, and the design method of static output feedback controller is presented. At the same time, the consistency problem of the system with interconnected parameter uncertainty and nonlinear parameter uncertainty is studied. The corresponding frequency-domain criterion, based on the time-domain criterion of LMI and the design method of static output feedback controller, are obtained. The consistency analysis and control of multi-interconnected dynamic network systems with communication delay and Markov random jump topology are carried out. The continuous Markov chain transfer rate matrix is considered to contain some unknown elements. First, the linear transformation matrix is used to transform the consistency problem of the network system, and then, for the system in each mode, the linear transformation matrix is used to transform the consistency problem of the network system. The consistency criteria based on bilinear matrix inequalities for linear systems and nonlinear systems are obtained by selecting appropriate Lyapunov-Krasovskii functional, and the static output feedback controller gain is obtained by iterative algorithm.
【学位授予单位】：北京工业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O157.5

【相似文献】