Normalization of homogeneous approximations of symmetric affine control systems with two controls

被引：2
|
作者：
Ignatovich, S. Yu. [1 ]
机构：
[1] Kharkov Natl Univ, Dept Differential Equat & Control, Kharkov, Ukraine
来源：
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2011年 / 17卷 / 01期
关键词：
Symmetric affine control system; homogeneous approximation; normal form; growth vector; core Lie subalgebra; CARNOT ALGEBRAS; CONTROLLABILITY; CLASSIFICATION; NILPOTENT;
D O I：
10.1007/s10883-011-9109-0
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we study properties of growth vectors and homogeneous approximations of symmetric affine control systems. We say that a growth vector is A-normal if homogeneous approximations of all systems with this growth vector can be reduced (by use of feedbacks) to a finite number of "normal forms," and a growth vector is said to be A-simple if the set of homogeneous approximations of all small perturbations of systems with this growth vector satisfies this property. We give the complete description of A-normal and A-simple growth vectors for systems with two-dimensional controls. As the main tool, we develop the free algebraic technique.
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页码：1 / 48
页数：48
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