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Stationary Bifurcations Control with Applications

Stationary Bifurcations Control with Applications 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Stationary Bifurcations Control with Applications

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References (21)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media B.V.
Subject
Mathematics; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Computer Science, general; Mathematics, general
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-008-9361-9
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Nov 19, 2008

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