网络化鲁里叶系统的分布式控制研究

发布时间：2018-03-11 09:30

本文选题：鲁里叶系统　切入点：非线性网络　出处：《哈尔滨工业大学》2015年博士论文　论文类型：学位论文

【摘要】：由多个单系统(又称为智能体)以相互协作的方式组成的大规模网络化系统具有功能强大、灵活度高、成本低廉等优势,是编队航天器系统、多机器人系统、智能电网等工程问题的通用化理论模型。为实现网络化系统的协同工作,需要对网络中的各个成员进行分布式控制,以协同完成预定的目标任务。分布式控制的核心是,仅利用网络中相邻智能体间的(局部)相对信息,将动态网络的群体行为协调到期望的状态,如达到同步。对诸如考虑执行机构含有饱和或死区等区间非线性的航天器动力学,可以由鲁里叶系统来描述。因此,本论文针对节点动力学为鲁里叶系统的非线性多智能体网络,基于代数图论、绝对稳定性理论、线性矩阵不等式、鲁棒H∞/最优等控制技术,开展该类网络化系统的鲁棒同步问题研究,取得如下研究成果:针对能够由连通无向图表示的无领航者多鲁里叶系统,考虑经静态相对状态反馈分散耦合而成的动态网络鲁棒同步问题,提出了分别考虑增量无源鲁里叶非线性与增量扇区有界鲁里叶非线性下的完全分布式鲁棒同步算法。理论证明给出如下结论:任意连通无向图的拉普拉斯矩阵的非零特征根对应的特征向量张成的矩阵与其自身转置的乘积生成的矩阵为节点数相同的无权完全图的拉普拉斯矩阵。利用该结论构造无向鲁里叶网络的同步误差系统,分析该误差系统全局渐近稳定的充分条件,给出了静态相对状态反馈同步协议中反馈增益矩阵的设计方法。进一步,在上述静态相对状态反馈同步协议中引入自适应耦合权重,实现由局部同步误差驱动的各边权重的动态调整,理论分析证明,该时变权重的引入能够在无不知道完整网络拓扑结构的情况下实现无向鲁里叶网络的鲁棒同步。进一步针对强连通有向图的情况,设计了一种有向鲁里叶网络的鲁棒同步算法。基于强连通有向图的拉普拉斯矩阵对应零特征根的左特征向量,构造了同步误差系统及相应的李雅普诺夫函数,并利用强连通有向图的广义代数连通度证明了该误差系统的全局渐近稳定性,从而证明了所设计的同步算法是有效的。由于含有一条有向生成树的有向图总能划分成多个强连通子图,能够利用强连通图的相关结论给出由该有向图中所有根节点组成的强连通子图上的多鲁里叶系统同步的充分条件,再理论证明该有向图中其余节点上的鲁里叶系统可收敛于根节点的同步流型,从而给出含有一条有向生成树的有向鲁里叶网络的鲁棒同步算法。针对仅有相对测量输出信息可用的无向鲁里叶网络的鲁棒同步问题,考虑鲁里叶非线性未知的情况,提出了一种基于相对测量输出线性动态反馈同步协议的设计方法。在构造同步误差系统并分析其全局渐近稳定性的基础上,证明了同步协议参数矩阵需要满足的充分条件,进一步基于线性H∞控制技术,给出了这些参数矩阵的计算方法。由于我们所设计的同步协议是动态的,对其状态空间维数的选取也一并做了讨论。由于未对鲁里叶非线性作精确已知的假设,只需满足增量无源或增量扇区有界条件,我们所设计的同步协议在这个意义下是鲁棒的。由于实际网络化系统,如智能电网等中的节点动力学并不完全一致,为此假设所有鲁里叶系统的线性部分是一致的,而其非线性部分可以是不同的,引入输出调节理论,分别提出了基于动态状态反馈与动态输出反馈的异构鲁里叶网络的鲁棒输出同步协议设计方法。该方法采用分布式观测器技术,首先在含有一条有向生成树的有向网络上设计一个同构分布式观测器网络,在每个节点处渐近地复现一个共同的参考信号,然后基于输入状态稳定性理论,设计局部输出调节控制器现实各智能体对该参考信号的跟踪控制。由于分布式观测器的引入,使得局部输出调节控制器的设计不局限于鲁里叶系统,因此本方法可用于处理任意节点动态的异构网络同步问题。
[Abstract]:A single system (also called agent) large-scale networked system with mutual cooperation way has strong function, high flexibility, low cost and other advantages, is the formation of spacecraft system, multi robot system, smart grid and other engineering problems. A general theoretical model for collaborative work of network system the need for distributed control of each member of the network, in order to complete the objectives and tasks scheduled. Collaborative distributed control is the core, only the use of adjacent intelligent network between the (local) relative information, the group behavior coordination of dynamic network to the desired state, such as synchronization of Interval Nonlinear Dynamics of spacecraft. Such as considering actuator saturated or dead, by Ruriye to describe the system. Therefore, this thesis focuses on the node dynamics of nonlinear Lurie system of multi agent based network. In algebraic graph theory, the theory of absolute stability, linear matrix inequality, the robust H / optimal control technology, to carry out research on robust synchronization of the network system, the main achievements were as follows: the leader Doru Lee Ye system can be represented by undirected graph, considering the dynamic network robust synchronization problem by static state feedback decentralized coupled together, put forward respectively considering the incremental passive Lurie and incremental nonlinear sector bounded nonlinear Lurie under fully distributed robust synchronization algorithm. Theoretical proof is given as follows: arbitrary undirected non product feature vectors in a matrix with zero eigenvalues and its transpose matrix Laplasse matrix the figure for the same number of nodes to end the Laplasse matrix map. The synchronization error system to Lurie network using this conclusion structure, The error analysis of sufficient conditions for global asymptotic stability of the system, given the relatively static state feedback design method of feedback gain matrix synchronization protocol. Further, the introduction of adaptive weights in the coupled relative static state feedback synchronization protocol, to realize the dynamic adjustment of each edge weights by local synchronization error driven, theoretical analysis shows that the introduction of the when the variable weight can all know the complete network topology under the condition of non synchronization to robust Lurie network. Aiming at the strongly connected directed graph of the situation, has designed a robust synchronization algorithm to the network. Ruriye strongly connected directed left eigenvector matrix of the Laplasse graph corresponding to zero eigenvalue based on the structure of the synchronization error system and the corresponding Lyapunov function, and the use of strong connectivity to generalized algebraic connectivity of a proof of the error system The global asymptotic stability and synchronization algorithm so as to prove the design is effective. Because it contains a directed spanning tree directed graph is always divided into a plurality of strongly connected subgraph, leaf synchronization sufficient condition can by the composition of the root node to the graph all strongly connected subgraph with given conclusion the Shandong strongly connected graph, then it is proved that the synchronization pattern to other nodes on the Ruriye system diagram can converge to the root node, which is containing a directed spanning tree to robust synchronization algorithm of Lurie network. According to the only output information available without relative measurement to the problem of robust synchronization of Lur'e network, considering the nonlinear unknown Rury, presents a design method of measuring the relative output linear dynamic feedback synchronization protocol. Based on structural system and analyses its full synchronization error Based on the asymptotic stability of the Bureau, we establish sufficient conditions for the parameter matrix to satisfy the synchronization protocol, further based on linear H control technology, the calculation method of parameter matrix is given. The synchronization protocol designed by us is dynamic, the selection of the state space dimension are also discussed. Because of not accurate known for Lur'e nonlinear assumptions, only need to meet the incremental passive or incremental sector boundary conditions, we design the synchronization protocol is robust in this sense. Because of the actual network system, such as node dynamics in the smart grid is not exactly the same, so the assumption of linear part of all of the Ruriye system is consistent but, the nonlinear part can be different, the output regulation theory, respectively, proposed a dynamic state feedback and dynamic output feedback Lurie heterogeneous network based on Shandong Best output synchronization protocol design method. This method adopts distributed observer techniques, first in contains a directed spanning tree has designed a homogeneous distributed network to network observer, at each node asymptotically reproducing a common reference signal, then input state stability based on the theory, the design of local controller real output each agent of the reference signal tracking control. Due to the introduction of distributed observer, design the local controller output is not limited to Lurie system, so this method can be used to deal with heterogeneous network synchronization at any node dynamically.

【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O231.4

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