Stabilization of relative equilibria for underactuated systems on Riemannian manifolds

被引：38

作者：

Bullo, F

机构：

[1] Univ Illinois, Coordinated Sci Lab, Urbana, IL 61801 USA

[2] Univ Illinois, Dept Gen Engn, Urbana, IL 61801 USA

来源：

AUTOMATICA | 2000年 / 36卷 / 12期

关键词：

nonlinear control; mechanical-systems; exponentially stable; differential geometric methods;

D O I：

10.1016/S0005-1098(00)00115-1

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper describes a systematic procedure to exponentially stabilize relative equilibria of mechanical systems. We review the notion of relative equilibria and their stability in a Riemannian geometry context. Potential shaping and damping control are employed to obtain full exponential stabilization of the desired trajectory. Two necessary conditions are that the effective potential be positive definite over a specified subspace and that the system be linearly controllable. Relevant applications to underwater and aerospace vehicle control are described. (C) 2000 Elsevier Science Ltd. All rights reserved.

引用

页码：1819 / 1834

页数：16

共 50 条

[1] Quasivelocities and Stabilization of Relative Equilibria of Underactuated Nonholonomic Systems
Bloch, Anthony M.
Marsden, Jerrold E.
Zenkov, Dmitry V.
PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, : 3335 - 3340
[2] Reduction, Linearization, and Stability of Relative Equilibria for Mechanical Systems on Riemannian Manifolds
Francesco Bullo
Andrew D. Lewis
Acta Applicandae Mathematicae, 2007, 99 : 53 - 95
[3] Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds
Bullo, Francesco
Lewis, Andrew D.
ACTA APPLICANDAE MATHEMATICAE, 2007, 99 (01) : 53 - 95
[4] Unstable manifolds of relative equilibria in Hamiltonian systems with dissipation
Derks, G
Ratiu, T
NONLINEARITY, 2002, 15 (03) : 531 - 549
[5] Stabilization of relative equilibria
Jalnapurkar, SM
Marsden, JE
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2000, 45 (08) : 1483 - 1491
[6] Feedback stabilization of relative equilibria for mechanical systems with symmetry
Bloch, AM
Marsden, JE
deAlvarez, GS
CURRENT AND FUTURE DIRECTIONS IN APPLIED MATHEMATICS, 1997, : 43 - 64
[7] Relaxed matching for stabilization of relative equilibria of mechanical systems
Long, David
Zenkov, Dmitry V.
PROCEEDINGS OF THE 46TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2007, : 3044 - 3049
[8] RELATIVE ISOMETRIC EMBEDDINGS OF RIEMANNIAN MANIFOLDS
Ghomi, Mohammad
Greene, Robert E.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (01) : 63 - 73
[9] EQUILIBRIA ON L-RETRACTS IN RIEMANNIAN MANIFOLDS
Hosseini, Seyedehsomayeh
Pouryayevali, Mohamad R.
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2016, 47 (02) : 579 - 592
[10] Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups
Nordkvist, Nikolaj
Bullo, Francesco
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (11) : 2651 - 2658

← 1 2 3 4 5 →