摘要
本文的目的是描述与分析非线性控制系统的拓扑结构.文中首先定义可线性化系统,然后引入Whitney拓扑,并用此定义非线性控制系统族上的拓扑.在这个拓扑下,证明了除单输入二维系统外,在一般情况下能线性化的系统是一个零测集.最后讨论一般反馈线性化问题.对输入数仅比系统维数少一的情况给出了充要条件,并证明了在此情况下几乎所有的系统均可线性化.
This paper is devoted to the description and analysis of the topology of nonlinear control systems. First of all, we define linearizable systems. Secondly, the basic concepts of Whitney topology are introduced, and used to describe the topology of the collection of nonlinear control systems. Under this topology we have shown that lineaizable set is a measure zero set unless m=1 and n=2 with m the input number and n the dimension of the state space. Thirdly, we discuss the problem of general feedback linearization. Necessary and sufficient conditions are given when n=m+1. Finally, we show that when n=m+1, all systems but a measure zero set are linearizable.
出处
《自动化学报》
EI
CSCD
北大核心
1991年第2期129-136,共8页
Acta Automatica Sinica
关键词
控制系统
非线性
拓扑结构
Linearizable systems
whitney topology
general feedback control
