An invariant-manifold-based method for chaos control

Citation
Xh. Yu et al., An invariant-manifold-based method for chaos control, IEEE CIRC-I, 48(8), 2001, pp. 930-937
Citations number
21
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Eletrical & Eletronics Engineeing
Journal title
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS
ISSN journal
1057-7122 → ACNP
Volume
48
Issue
8
Year of publication
2001
Pages
930 - 937
Database
ISI
SICI code
1057-7122(200108)48:8<930:AIMFCC>2.0.ZU;2-D
Abstract
In this paper, we extend the OGY chaos-control method to be one based on th e invariant manifold theory and the sliding mode control concept. This exte nded-control method not only can deal with higher order chaotic systems in the same spirit of the OGY method, but also can remove the reliance of the control on eigenvalues and eigenvectors of the system Jacobians, resulting in an even simpler but more effective controller. The novelty of the new de sign lies in the construction of suitable invariant manifolds according to the desired dynamic properties. The controller is then forcing the system s tate to lie on the intersection of the selected invariant manifolds, so tha t once the invariant manifolds are reached, the chaotic system will be guid ed toward a desired fixed point that corresponds to an originally targeted unstable periodic orbit of the given system. Such an idea is directly relev ant to the sliding mode control approach. This new method is particularly u seful for controlling higher order chaotic systems, especially in the case where some of the eigenvalues of the system Jacobian are complex conjugates . The effectiveness of the proposed method is tested by numerical examples of the third-order continuous-time Lorenz system and the fourth-order discr ete-time double rotor map.