多个体系统牵引控制下的能控性

发布时间：2018-05-08 15:20

本文选题：多个体系统 + 能控性　；参考：《南京师范大学》2017年硕士论文

【摘要】：多个体系统是具有一定网络结构的一组动态系统.从数学模型上来看,多个体系统就是一组具有图结构的微分方程组或者差分方程组.多个体系统控制理论有广泛的应用背景,比如机器人群的协作,无人机群的编队以及卫星群的姿态同步.多个体系统控制理论扩展了传统单个体系统的控制理论,是结合了图论、微分方程理论和控制理论的一个新的研究分支.多个体系统的牵引控制就是通过控制动态网络中的某些节点来控制整个系统的行为.能控性是动态系统控制理论中的一个基本概念,它反映了外部输入对系统行为的控制能力.多个体系统在牵引控制下的能控性则是探究能否通过牵制部分节点来实现对整个动态网络的控制能力,它正在逐步发展成为一个新的研究热点.本文主要研究了线性多个体控制系统在牵引控制下的能控性问题.首先建立了一个一般形式的数学模型,该模型涵盖了已有文献中的模型,并将已有的结果推广到了这个一般化模型中,得到了能控性的必要条件以及充分条件.其次针对一些具体的网络结构包括圈图、完全图、星状图及Petersen图,给出了牵引控制的设计,并对能控性给出了证明.
[Abstract]:Multi-individual system is a group of dynamic systems with a certain network structure. From the mathematical model, the multi-individual system is a group of differential equations or difference equations with graph structure. The theory of multi-individual system control has a wide application background, such as the cooperation of robot crowd, the formation of UAV and the attitude synchronization of satellite group. The control theory of multi-individual systems extends the control theory of traditional single-individual systems and is a new branch of research which combines graph theory differential equation theory and control theory. The traction control of multi-individual system controls the behavior of the whole system by controlling some nodes in the dynamic network. Controllability is a basic concept in dynamic system control theory, which reflects the ability of external input to control system behavior. The controllability of multi-individual system under traction control is to explore whether the control ability of the whole dynamic network can be realized by restraining some nodes, and it is gradually developing into a new research hotspot. In this paper, the controllability of linear multi-individual control system under traction control is studied. Firstly, a general mathematical model is established, which covers the existing models in the literature, and extends the existing results to the generalized model. The necessary conditions and sufficient conditions for controllability are obtained. Secondly, the design of traction control is given and the controllability is proved for some specific network structure including cycle graph, complete graph, star graph and Petersen diagram.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O231

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