Adaptive Controller Design for Full State Hybrid Projective Synchronization of Uncertain Hyperchaotic Systems

In this paper, a simple adaptive control scheme is developed to study the full state hybrid projective synchronization (FSHPS) behavior between two identical hyper chaotic systems with unknown parameters. The adaptive FSHPS controllers are designed based on Lyapunov stability theorem and an analytic expression of the controllers with the adaptive laws of parameters are presented. The adaptive controllers can be simplified ulteriorly such that it is not necessary to exert controllers on all the variables to achieve complete synchronization. The experimental results show that parameters identification and FSHPS of two hyper chaotic systems can be realized simultaneously. The proposed methods have certain significance for reducing the cost and complexity for controller implementation.