A characterization of the Lie algebra rank condition by transverse periodic functions

被引：49

作者：

Morin, P ^{[1
]}

Samson, C ^{[1
]}

机构：

[1] INRIA, F-06902 Sophia Antipolis, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2001年 / 40卷 / 04期

关键词：

controllability; driftless system; transversality; Lie algebra;

D O I：

10.1137/S0363012900366054

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The Lie algebra rank condition plays a central role in nonlinear systems control theory. The present paper establishes that the satisfaction of this condition by a set of smooth control vector fields is equivalent to the existence of smooth transverse periodic functions. The proof here enclosed is constructive and provides an explicit method for the synthesis of such functions.

引用

页码：1227 / 1249

页数：23

共 19 条

[1]

Abraham R., 2012, Manifolds, tensor analysis, and applications, V75

[2]

Chow W-L., 1939, MATH ANN, V117, P98, DOI [DOI 10.1007/BF01450011, 10.1007/BF01450011]

[3]

Dixon WE, 2000, INT J ROBUST NONLIN, V10, P199, DOI 10.1002/(SICI)1099-1239(20000415)10:4<199::AID-RNC468>3.0.CO

[4]

2-P

[5]

HERMANN R, 1963, P INT S NONL DIFF EQ, P325

[6] NILPOTENT AND HIGH-ORDER APPROXIMATIONS OF VECTOR FIELD SYSTEMS [J].

HERMES, H .

SIAM REVIEW, 1991, 33 (02) :238-264

[7]

Kawski M, 1998, MONOGR TXB PURE APPL, V207, P305

[8]

KAWSKI M, 1990, CONTR-THEOR ADV TECH, V6, P497

[9]

KAWSKI M, 1997, OPERATORS SYSTEMS LI, P111, DOI DOI 10.1007/978-3-663-09823-2_10

[10] An approximation algorithm for nonholonomic systems [J].

Liu, WS .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1997, 35 (04) :1328-1365

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