Function vector synchronization based on fuzzy control for uncertain chaotic systems with dead-zone nonlinearities

In this paper, a fuzzy adaptive control scheme is designed to achieve a function vector synchronization behavior between two chaotic (or hyperchaotic) systems in presence of unknown dynamic disturbances and input nonlinearities. This synchronization can be considered as a generalization of many existing projective synchronization (namely the function projective synchronization, the modified projective synchronization, generalized projective synchronization and so on) 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. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop system as well as the exponential convergence of the synchronization errors to an adjustable region. The synchronization between Lorenz and Chen chaotic systems is taken as an illustrative example to show the effectiveness of the proposed method.