Generalized synchronization of different orders of chaotic systems. with unknown parameters and parameter identification

Using add-order method to translate the problem of generalized synchronization of different orders of chaotic systems into the synchronization of systems of identical order. Based on Lyapunov stability theory and adaptive control method, we give the expression of adaptive controller and the updating rule of parameters, then achieve generalized synchronization of different order of chaotic systems with unknown parameters and enable the estimation of the parameters of the drive and the response systems. This method has been applied to solve the generalized synchronization problem of hyperchaotic Lu system, Lorenz system, generalized Lorenz system, and Liu system with unknown parameters. It is proved theoretically that this method is feasible. Numerical simulations show the effectiveness of the adaptive control technique.