Abstract
This chapter deals with adaptive fuzzy control-based function vector synchronization between two chaotic systems with both unknown dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities). This synchronization scheme can be considered as a natural generalization of many existing projective synchronization systems (namely the function projective synchronization, the modified projective synchronization, the projective synchronization and so on). To effectively deal with the input nonlinearities, the control system is designed in a variable-structure framework. In order to approximate uncertain nonlinear functions, the adaptive fuzzy systems are incorporated in this control system. A Lyapunov approach is used to prove the boundedness of all signals as well as the exponential convergence of the corresponding synchronization errors to an adjustable region. The synchronization between two chaotic satellite systems is taken as an illustrative example to show the effectiveness of the proposed synchronization method.