Generalized Synchronization of Hyperchaotic Systems with Unknown Parameters Using Adaptive Control

This paper studies the generalized synchronization for two identical or different hyperchaotic systems. A systematic adaptive control scheme is proposed in case systems´ parameters cannot be exactly known a priori to tackle the effects of parameters´ uncertainties. Based on Lyapunov stability theory, an adaptive controller and the update laws of parameters are developed even the orders of the two systems are different. Two examples illustrate the effectiveness of the proposed control strategies. The simulation results indicate that the update laws of parameters are convergent and the update laws of parameters are also the parameters´ identifiers when the synchronization occurs between two identical systems.