Nonlinear Superposition Formulas for Two Classes of Non-holonomic Systems

被引：3

作者：

Menini, Laura ^{[1
]}

Tornambe, Antonio ^{[1
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Ingn Civile & Ingn Informat, I-00133 Rome, Italy

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2014年 / 20卷 / 03期

关键词：

Nonlinear superposition principle; Non-holonomic systems; Lie systems; DIFFERENTIAL-EQUATIONS; STABILITY ANALYSIS; PLANAR SYSTEMS; LIE; THEOREM; MOTION; RULES;

D O I：

10.1007/s10883-014-9225-8

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 aim of this paper is to apply the nonlinear superposition principle to some non-holonomic systems, in particular, those in chained and power forms, which are used to represent the kinematic equations of various non-holonomic wheeled vehicles. The existence of nonlinear superposition formulas is studied on the basis of Lie algebraic analysis. First, it is shown that nonlinear superposition formulas can be constructed using the knowledge of n + 1 particular solutions, using the affine structure of a system in chained form and the fact that a system in power form is diffeomorphic to a system in chained form. Secondly, using the notion of first integral, it is shown that only one particular solution is sufficient.

引用

页码：365 / 382

页数：18

共 50 条

[41] The non-holonomic double pendulum: An example of non-linear non-holonomic system
Sergio Benenti
Regular and Chaotic Dynamics, 2011, 16 : 417 - 442
[42] One invariant measure and different poisson brackets for two non-holonomic systems
Andrey V. Tsiganov
Regular and Chaotic Dynamics, 2012, 17 : 72 - 96
[43] The Non-holonomic Double Pendulum: an Example of Non-linear Non-holonomic System
Benenti, Sergio
REGULAR & CHAOTIC DYNAMICS, 2011, 16 (05): : 417 - 442
[44] On non-holonomic connexions
Schouten, JA
PROCEEDINGS OF THE KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, 1928, 31 (1/5): : 291 - 299
[45] One invariant measure and different poisson brackets for two non-holonomic systems
Tsiganov, Andrey V.
REGULAR & CHAOTIC DYNAMICS, 2012, 17 (01): : 72 - 96
[46] Non-holonomic integrators
Cortés, J
Martínez, S
NONLINEARITY, 2001, 14 (05) : 1365 - 1392
[47] Two non-holonomic lattice walks in the quarter plane
Mishna, Marni
Rechnitzer, Andrew
THEORETICAL COMPUTER SCIENCE, 2009, 410 (38-40) : 3616 - 3630
[48] Exponential stabilization of non-holonomic systems: an ENI approach
Huo, W
Ge, SS
INTERNATIONAL JOURNAL OF CONTROL, 2001, 74 (15) : 1492 - 1500
[49] Kinematic and Dynamic Singularities of Non-holonomic Robotic Systems
Tchon, Krzysztof
Ratajczak, Joanna
2017 11TH INTERNATIONAL WORKSHOP ON ROBOT MOTION AND CONTROL (ROMOCO), 2017, : 148 - 153
[50] The controllability of non-holonomic mechanical systems with constrained controls
1600, Elsevier Ltd (68):

← 1 2 3 4 5 →