A generalized function projective synchronization scheme for uncertain chaotic systems subject to input nonlinearities

• Published in: International journal of general systems Vol. 45; no. 6; pp. 689 - 710
• Main Authors: Hamel, Sarah, Boulkroune, Abdesselem
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 17.08.2016; Taylor & Francis LLC
• Subjects: Adaptive control; Adjustable; Chaos theory; Control systems; Control systems design; dead-zone; Dynamical systems; Function projective synchronization; fuzzy adaptive control; Fuzzy control; Fuzzy systems; Nonlinear dynamics; Nonlinearity; Scaling factors; sector nonlinearity; Synchronism; Synchronization; uncertain chaotic system
• ISSN: 0308-1079; 1563-5104
• DOI: 10.1080/03081079.2015.1118094

In this paper, a modified generalized function projective synchronization scheme for a class of master-slave chaotic systems subject to dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities) is investigated. This synchronization system can be seen as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization and so on), in the sense that the master system has a scaling function matrix and the slave system has a scaling factor matrix. To practically achieve this generalized function synchronization, an adaptive fuzzy variable-structure control system is designed. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the synchronization errors to an adjustable region. Simulations results are presented to illustrate the effectiveness of the proposed generalized function PS scheme.