Necessary and sufficient condition for global controllability of planar affine nonlinear systems

被引：23
作者：
Sun, Yimin [1 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2007年 / 52卷 / 08期
基金：
中国国家自然科学基金;
关键词：
affine nonlinear systems; control curve; global controllability; Jordan curve theorem; reachable set;
D O I：
10.1109/TAC.2007.902750
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 correspondence, we will investigate the global controllability of general planar affine nonlinear systems, and present a simple necessary and sufficient condition for global controllability. The analysis is carried out in detail, which is based on some basic facts in planar topology such as the Jordan curve Theorem, and in the geometrical theory of ordinary differential equations including the Poincare-Bendixson Theorem. Furthermore, we will also discuss the global controllability for higher dimensional affine nonlinear system with a triangular-like structure.
引用
收藏
页码：1454 / 1460
页数：7
相关论文
共 34 条
[11]  
Emel'yanov S. V., 1988, Soviet Physics - Doklady, V33, P400
[12]  
Emel'yanov S. V., 1988, Soviet Physics - Doklady, V33, P167
[13]  
Fulton W., 1995, Graduate Texts in Mathematics, V153
[14]  
HARTMAN P, 1982, ORDINARY DIFFERENTIA, P25
[15]   NONLINEAR CONTROLLABILITY VIA LIE THEORY [J].
HAYNES, GW ;
HERMES, H .
SIAM JOURNAL ON CONTROL, 1970, 8 (04) :450-&
[16]   NONLINEAR CONTROLLABILITY AND OBSERVABILITY [J].
HERMANN, R ;
KRENER, AJ .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1977, 22 (05) :728-740
[17]   LOCAL AND GLOBAL CONTROLLABILITY [J].
HERMES, H .
SIAM JOURNAL ON CONTROL, 1974, 12 (02) :252-261
[18]   GLOBAL-CONTROLLABILITY OF LOCALLY LINEARIZABLE SYSTEMS [J].
HIRSCHORN, RM .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1990, 28 (03) :540-551
[19]   N-DIMENSIONAL CONTROLLABILITY WITH (N-1) CONTROLS [J].
HUNT, LR .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1982, 27 (01) :113-117
[20]  
HUNT LR, 1980, MATH SYST THEORY, V13, P361
1234