ENERGY SHAPING FOR SYSTEMS WITH TWO DEGREES OF UNDERACTUATION AND MORE THAN THREE DEGREES OF FREEDOM

被引：9

作者：

Ng, Wai Man ^{[1
]}

Chang, Dong Eui ^{[1
]}

Labahn, George ^{[2
]}

机构：

[1] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

[2] Univ Waterloo, Cheriton Sch Comp Sci, Waterloo, ON N2L 3G1, Canada

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2013年 / 51卷 / 02期

关键词：

controlled Lagrangian; energy shaping; matching conditions; stabilizability; MECHANICAL SYSTEMS; CONTROLLED LAGRANGIANS; STABILIZATION;

D O I：

10.1137/11084995X

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study the stabilizability, via the method of energy shaping, of a given Lagrangian system with two degrees of underactuation and with n >= 4 degrees of freedom. By making use of the formal theory of PDEs, we derive an involutive system of PDEs which governs energy shapability, and thus deduce, for the first time, easily verifiable conditions under which energy shaping is guaranteed. We illustrate our results with an example of a three-cart-one-inverted pendulum system.

引用

页码：881 / 905

页数：25

共 50 条

[1] Energy shaping control for systems with underactuation degrees two by controlled Lagrangian method
Liu, Ce
[J]. INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2022, 32 (06) : 3485 - 3510
[2] Dynamical Tunneling in More than Two Degrees of Freedom
Keshavamurthy, Srihari
[J]. ENTROPY, 2024, 26 (04)
[3] On certain periodic motions of dynamical systems with more than two degrees of freedom
Lewis, DC
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1934, 56 : 25 - 41
[4] CHAOTIC SCATTERING IN SYSTEMS WITH MORE THAN 2 DEGREES OF FREEDOM
DING, MZ
OTT, E
[J]. THREE-DIMENSIONAL SYSTEMS, 1995, 751 : 182 - 204
[5] DISAPPEARANCE OF INTEGRALS IN SYSTEMS OF MORE THAN 2 DEGREES OF FREEDOM
CONTOPOULOS, G
[J]. CELESTIAL MECHANICS, 1978, 17 (02): : 167 - 172
[6] Integrable Systems with Dissipation and Two and Three Degrees of Freedom
Shamolin M.V.
[J]. Journal of Mathematical Sciences, 2018, 235 (2) : 220 - 242
[7] Localization of energy in nonlinear systems with two degrees of freedom
Koz'min, A. Yu.
Mikhlin, Yu. V.
Pierre, C.
[J]. INTERNATIONAL APPLIED MECHANICS, 2007, 43 (05) : 568 - 576
[8] Localization of energy in nonlinear systems with two degrees of freedom
A. Yu. Koz’min
Yu. V. Mikhlin
C. Pierre
[J]. International Applied Mechanics, 2007, 43 : 568 - 576
[9] On the Dynamics of Systems with Two Degrees of Freedom
N. V. Denisova
[J]. Doklady Mathematics, 2022, 105 : 1 - 5
[10] Dynamical systems with two degrees of freedom
Birkhoff, GD
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1917, 3 : 314 - 316

← 1 2 3 4 5 →