微分几何在非线性系统中的应用  

Applications of Differential Geometry in Nonlinear Systems

作　　者：赵建红[1] 宋芳芳[1] 

机构地区：[1]通化师范学院数学系,吉林通化134002

出　　处：《通化师范学院学报》2010年第4期11-12,共2页Journal of Tonghua Normal University

基　　金：吉林省教育厅科技项目(吉教科合字〔2009〕第470号)

摘　　要：微分几何方法作为一种新的工具,被引入控制系统特别是非线性控制系统的研究中,并得到很大发展.文中在两个不同方面就此问题进行了讨论.首先,针对非线性振动系统的模态研究,探讨模态的几何性质,以期赋予非线性模态一个更加直观的几何意义;其次,介绍基于微分几何理论,通过非线性状态反馈和非线性坐标变换实现非线性系统的完全线性化的方法.Differential geometry as a new tool is introduced to the control system, particularly the study of nonlinear control systems, and has derived great development. In this paper, two different aspects of this problem are discussed. Firstly, the geometric nature of the modality is discussed for nonlinear vibratory system to give a more intuitive geometric significance; secondly, based on the theory of differential geometry, the complete linearization method for nonlinear systems by means of nonlinear state feedback and nonlinear coordinate transformation is proposed.

关 键 词：微分几何法 非线性系统 非线性模态 完全线性化 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]