摘要
对一类非线性控制系统可以先通过等价转换为三角形式非线性系统,然后通过后推法和前推法设计控制器.故而考察在线性坐标变换和状态反馈之下,给定仿射非线性系统是否等价于严格上三角形式,下三角形式系统和上对角系统.利用微分几何控制理论,给出非线性系统等价于上述三种特定系统的充分必要条件.最后,用一个实例说明如何通过状态反馈和线性坐标变换实现上述等价转换.
For a class of nonlinear control system, one may transform it to a triangular nonlinear systems equivalently, and then design the controllers of the triangular systems by using the techniques of backstepping and forwarding. So the problems of whether a given affine nonlinear system is equivalent to a strict upper-triangular system, a low-triangular system and an upper-diagonal system via linear coordinate transformations and state feedback are considered. By using the differential geometric control theory, the necessary and sufficient conditions under which the nonlinear systems are equivalent to those three special systems above mentioned via linear coordinate transformations and feedback are presented. An example is given to illustrate on how to realize those equivalent transformations via linear coordinate conversions and a state feedback.
出处
《系统科学与数学》
CSCD
北大核心
2015年第7期802-811,共10页
Journal of Systems Science and Mathematical Sciences
基金
国家支撑计划(2013BAF07B03)资助课题
关键词
非线性系统
线性坐标变换
三角形式系统.
Nonlinear systems, linear coordinate transformations, triangular sys-tems.
