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Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control
Author
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-12-02
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
Standard adaptive control is the preferred approach for stabilization and synchronization of chaotic systems when the structure of such systems is a priori known but the parameters are unknown.
However, in the presence of unmodeled dynamics and/or disturbance, this approach is not effective anymore due to the drift of the parameter estimations, which eventually causes the instability of the closed-loop system.
In this paper, a robustifying term, which consists of a saturation function, is used to avoid this problem.
The robustifying term is added to the adaptive control law.
Consequently, the learning law is also modified.
The boundedness of the states and the parameter estimations is rigorously and thoroughly proven by means of Lyapunov like analysis based on Barbalat’s lemma.
On these new conditions, the convergence to zero cannot be achieved due to the presence of unmodeled dynamics and/or disturbance.
However, it is still possible to guarantee the asymptotic convergence to a bounded zone around zero.
The width of this zone can be adjusted by the designer.
The performance of this robust approach is verified by numerical simulations.
Although, for simplicity, this strategy is only applied to the stabilization and synchronization of Zhang system, the procedure can easily be generalized to a broad class of chaotic systems.
American Psychological Association (APA)
Pérez-Cruz, J. Humberto. 2018. Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control. Complexity،Vol. 2018, no. 2018, pp.1-19.
https://search.emarefa.net/detail/BIM-1134475
Modern Language Association (MLA)
Pérez-Cruz, J. Humberto. Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control. Complexity No. 2018 (2018), pp.1-19.
https://search.emarefa.net/detail/BIM-1134475
American Medical Association (AMA)
Pérez-Cruz, J. Humberto. Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control. Complexity. 2018. Vol. 2018, no. 2018, pp.1-19.
https://search.emarefa.net/detail/BIM-1134475
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1134475