Access the full text.
Sign up today, get DeepDyve free for 14 days.
E. Abed, Jyun-Horng Fu (1987)
Local feedback stabilization and bifurcation control, II. Stationary bifurcationSystems & Control Letters, 8
W. Kang (1997)
Invariants and stability of control systems with transcritical and saddle-node bifurcationsProceedings of the 36th IEEE Conference on Decision and Control, 2
Guanrong Chen (1999)
Controlling Chaos and Bifurcations in Engineering Systems
G. Gu, X. Chen, A.G. Sparks, S.S. Banda (1999)
Bifurcation stabilization with local output feedbackSIAM J. Control Optim., 37
K. Furuta, Masaki Yamakita, S. Kobayashi (1992)
Swing-up Control of Inverted Pendulum Using Pseudo-State FeedbackProceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 206
G. Brown, R. Hancock, R. Cooper (1992)
In Situ Decommissioning—the Radical Approach for Nuclear Power StationsProceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 206
F. Verduzco (2004)
Controlling from the center manifold codimension one bifurcations2004 5th Asian Control Conference (IEEE Cat. No.04EX904), 1
Guanrong Chen, J. Moiola, Hua Wang (2000)
Bifurcation Control: Theories, Methods, and ApplicationsInt. J. Bifurc. Chaos, 10
F. Verduzco, J. Alvarez (1999)
BIFURCATION ANALYSIS OF A 2-DOF ROBOT MANIPULATOR DRIVEN BY CONSTANT TORQUESInternational Journal of Bifurcation and Chaos, 09
W. Kang (1998)
Bifurcation and Normal Form of Nonlinear Control Systems, Part IISiam Journal on Control and Optimization, 36
S. Wiggins (1989)
Introduction to Applied Nonlinear Dynamical Systems and Chaos
F. Colonius, L. Grüne (2002)
Dynamics, Bifurcations and Control
Taihyun Kim, E. Abed (2001)
Stationary bifurcation control of systems with uncontrollable linearizationInternational Journal of Control, 74
F. Verduzco (2007)
Control of codimension One Stationary bifurcationsInt. J. Bifurc. Chaos, 17
W. Levine (2010)
The Control Handbook
W. Kang, Ke Liang (1997)
The stability and invariants of control systems with pitchfork or cusp bifurcationsProceedings of the 36th IEEE Conference on Decision and Control, 1
L. Perko (1998)
Differential Equations and Dynamical Systems
D. Hill, Guanrong Chen, Xinghuo Yu (2003)
Bifurcation Control: Theory and Applications
F. Verduzco (2004)
Control of the saddle-node and transcritical bifurcationsIFAC Proceedings Volumes, 37
G. Gu, Xiang Chen, A. Sparks, S. Banda (1997)
Bifurcation stabilization with local output feedbackProceedings of the 1997 American Control Conference (Cat. No.97CH36041), 3
Jyun-Horng Fu, E. Abed (1993)
Linear feedback stabilization of nonlinear systems with an uncontrollable critical modeAutom., 29
Given a family of nonlinear control systems, where the Jacobian of the driver vector field at one equilibrium has a simple zero eigenvalue, with no other eigenvalues on the imaginary axis, we split it into two parts, one of them being a generic family, where it is possible to control the stationary bifurcations: saddle-node, transcritical and pitchfork bifurcations, and the other one being a non-generic family, where it is possible to control the transcritical and pitchfork bifurcations. The polynomial control laws designed are given in terms of the original control system. The center manifold theory is used to simplify the analysis to dimension one. Finally, the results obtained are applied to two underactuated mechanical systems: the pendubot and the pendulum of Furuta.
Acta Applicandae Mathematicae – Springer Journals
Published: Nov 19, 2008
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.