一类多项式仿射非线性系统的全局能控性.docVIP

n 一类多项式仿射非线性系统的全局能控性 孙轶民1 1 中山大学数学与计算科学学院广东省计算科学重点实验室, 广州, 510275 摘要：本文对一类具有特殊结构的低维多项式仿射非线性系统给出其全局能控性的充分必要条 件. 这个条件只施加在系统的系数上. 证明方法是基于格林公式和平面线性系统的轨线分析. 进 一步, 我们也指出对相应的高维多项式系统, 其全局能控性不再拥有. 关键词：控制理论, 仿射非线性, 多项式系统, 全局能控性, 格林公式 中图分类号： O231.2 On Global Controllability for a Class of Polynomial A?ne Nonlinear Systems SUN Yimin 1 1 Guangdong Province Key Laboratory of Computational Science, School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou, 510275 Abstract: In this paper, a necessary and su?cient condition of the global controllability for a class of low dimensional polynomial a?ne nonlinear systems with special structure is obtained. The condition is imposed on the coe?cients of the system only and the methods are based on Green’s formula and the trajectory analysis of planar linear system. Furthermore, we point out that the global controllability does not hold for the corresponding high dimensional polynomial system. Key words: Control theory, A?ne nonlinearity, polynomial system, global controllability, Green’s Formula. 0 Introduction As a fundamental concept in control theory, controllability has been investigated exten- sively since 1960. For linear control systems, their controllability had already been completely solved in 1960s and become the standard results in textbooks, see [1, 2]. Since 1970, the controllability of nonlinear systems has attracted much attention of many researchers in the ?eld of control theory and control engineering, and signi?cant progress has been made by in- troducing some useful mathematical methods, including the well-known di?erential geometric 基金项目： Natural Science Foundation of China No. Ph.D Programs Foundation of Ministry of Education of China and Fundamental Research Funds for the Central Universities. 作者简介： Yimin Sun, male, associate professor, email: sunyimin@amss.ac.cn. -1- n methods, see, for example, [3]-[6]. However, most of the existing results in the literature on the cont