Function vector synchronization based on fuzzy control for uncertain chaotic systems with dead‐zone nonlinearities. (26th November 2015)

• Record Type: Journal Article
• Authors: Hamel, Sarah; Boulkroune, Abdesselem; Bouzeriba, Amel
• Is Part Of: Complexity. Volume 21(2016)Supplement 1
• Page Start: 234
• Page End: 249
• Publication Date: 2015-11-26
• Subjects: fuzzy control -- function vector synchronization -- chaotic satellite system -- uncertain chaotic system -- input nonlinearities; Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1002/cplx.21737
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : In this article, a fuzzy adaptive control scheme is designed to achieve a function vector synchronization behavior between two identical or different chaotic (or hyperchaotic) systems in the presence of unknown dynamic disturbances and input nonlinearities (dead‐zone and sector nonlinearities). This proposed synchronization scheme can be considered as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization, generalized projective synchronization, and so forth) in the sense that the master and slave outputs are assumed to be some general function vectors. To practically deal with the input nonlinearities, the adaptive fuzzy control system is designed in a variable‐structure framework. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is used to prove the boundedness of all signals of the closed‐loop control system as well as the exponential convergence of the corresponding synchronization errors to an adjustable region. The synchronization between two identical systems (chaotic satellite systems) and two different systems (chaotic Chen and Lü systems) are taken as two illustrative examples to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 234–249, 2016