网络系统的牵引同步控制与滑模控制研究

发布时间：2018-03-29 09:39

本文选题：复杂网络　切入点：牵引同步　出处：《东南大学》2017年硕士论文

【摘要】：随着网络科学与先进控制技术的迅速发展,控制科学,特别是与其相关的一些交叉学科,如电气自动化、计算机科学、电子信息工程等,正日益受到越来越多的科研工作者的密切关注。通过控制理论来研究复杂网络的同步问题以及动态系统的稳定性、收敛性等问题,这是控制理论在网络科学中的一个重要应用。常见的控制方法有牵引控制、滑模变结构控制等。在研究复杂网络的同步控制问题时,通过牵引策略,只需合理地选取部分网络节点并对其施加控制,即可实现全部网络节点的同步,从而大大地降低对网络拓扑结构连通性的要求。控制理论在解决工程问题时同样有着重要的作用,事实上,很多工程问题所涉及的数学模型可采用微分系统来刻画;然而在实际应用中,系统不可避免地会受到一些不确定性因素的影响,如非线性外部干扰、测量误差等。滑模变结构控制作为一种重要的控制方法具有许多优良的性质,如对系统参数变化不敏感性、对外界干扰具有有效抵抗性以及控制简单易操作性等,因此在运用控制理论解决工程问题时,时常采用滑模变结构控制的方法。稳定性是控制理论研究的基本问题之一,对于网络节点同步问题的研究最终要归结到网络节点与目标节点所产生的误差动态系统的稳定性问题上来。本文主要致力于网络牵引同步控制问题的研究,并且通过滑模变结构控制使得系统具有良好的鲁棒性。基于此,本文主要的工作如下:(1)研究了一类带有Lorenz型节点和周期间歇通讯的有向动态复杂网络的牵引同步控制问题。通过利用Lyapunov稳定性理论以及M-矩阵理论,得到一组使整体网络达到牵引同步的判据;并给出如何选取系统的牵引节点的算法,以及求出拟施加牵引控制的系统节点的最小数目。通过理论分析证明:当系统的增强拓扑至少含有一个有向生成树,且系统节点之间的通讯率大于一个阈值以及系统邻接节点之间的耦合强度大于某一常数时,可以实现上述动态复杂网络的全局牵引同步。最后,通过一个仿真算例对所得理论结果进行了验证。(2)借鉴有限时间滑模控制及二阶固定时间滑模控制的方法,本文致力于研究高阶线性扰动系统的固定时间滑模控制问题。通过构造一列递归固定时间滑模面,并合理地设计固定时间滑模控制律,使得所研究的高阶系统实现固定时间稳定。在设计高阶固定时间收敛控制律时,本文通过限制系统状态变量的初始条件来保证控制律的有界性,从而有效地避免了控制律出现奇异性现象的问题。
[Abstract]:With the rapid development of network science and advanced control technology, control science, especially some related interdisciplinary disciplines, such as electrical automation, computer science, electronic information engineering, etc. More and more researchers are paying more and more attention to the synchronization of complex networks and the stability and convergence of dynamic systems by means of control theory. This is an important application of control theory in network science. The common control methods are traction control, sliding mode variable structure control and so on. The synchronization of all network nodes can be realized only by reasonably selecting some network nodes and applying control to them. Control theory also plays an important role in solving engineering problems. In fact, many mathematical models involved in engineering problems can be described by differential systems. However, in practical application, the system will inevitably be affected by some uncertain factors, such as nonlinear external disturbance, measurement error, etc. As an important control method, sliding mode variable structure control has many excellent properties. For example, it is insensitive to system parameters, resistant to external disturbance, and easy to control. Therefore, when using control theory to solve engineering problems, Sliding mode variable structure control is often used. Stability is one of the basic problems in control theory. The research on the synchronization problem of network nodes comes down to the stability of error dynamic systems caused by network nodes and target nodes. This paper is mainly devoted to the study of network traction synchronization control problem. And the sliding mode variable structure control makes the system robust. The main work of this paper is as follows: (1) the traction synchronization control problem for a class of directed dynamic complex networks with Lorenz nodes and periodic intermittent communication is studied. By using Lyapunov stability theory and M- matrix theory, A set of criteria for the traction synchronization of the whole network is obtained, and the algorithm of how to select the traction nodes of the system is given. And the minimum number of nodes in the system to be applied to traction control is obtained. It is proved by theoretical analysis that when the system's enhanced topology contains at least one directed spanning tree, When the communication rate between the system nodes is greater than a threshold and the coupling strength between the adjacent nodes is greater than a constant, the global traction synchronization of the dynamic complex network can be realized. The theoretical results obtained are verified by a simulation example. The method of finite time sliding mode control and second order fixed time sliding mode control is used for reference. In this paper, the fixed time sliding mode control problem for high order linear disturbance systems is studied. By constructing a set of recurrent fixed time sliding mode surfaces, a fixed time sliding mode control law is reasonably designed. In the design of the high order fixed time convergence control law, the boundedness of the control law is guaranteed by limiting the initial conditions of the system state variables. Thus the singularity of the control law is avoided effectively.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;O231

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